Grade 5 · 4.MD.A.2 · 2.MD.C.8

Money written as decimals

A price sticker at a garage sale says 4.75. How can one number say “four dollars” and “seventy-five cents” at the same time?

You need

MoneyGrade 2 Adding and subtracting decimalsGrade 5 Decimal place valueGrades 4 to 5

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Currency exchangeMath 7

Where you are 13 in Time and money

Measurement12

Time and money13

▴ 8 above Time zones Counting mixed coins

Money written as decimals

Story problems with dollars and cents Currency exchange

Why this exists

Advika, Kunle and Soledad are running a garage sale. Every table holds old toys, books and lamps, and every item needs a price sticker. Kunle has also emptied his piggy bank to see what he can buy: a few dollar bills and a pile of quarters, dimes and pennies.

Money comes in pieces of very different sizes. A dollar bill is worth 100 pennies. A price such as “four dollars and seventy-five cents” uses two units at once, and two units make adding hard: you would have to add the dollars, add the cents, and then trade 100 cents for a dollar whenever the cents got too big.

Decimal notation fixes this. It writes the whole amount as one number of dollars, with the cents as the part after the point. Then every money sum and difference is just adding and subtracting decimals, with the same lined-up columns and the same trades of ten for one.

Definition

One dollar is 100 cents. So one cent is one hundredth of a dollar:

1 \text{ cent} = \tfrac{1}{100} \text{ dollar} = 0.01 \text{ dollar}

An amount of money written as a decimal counts dollars. The whole number part is the number of dollars, and the two digits after the point are the cents. The dollar sign goes in front of the number, so \text{\textdollar}4.75 is read “four dollars and seventy-five cents”.

An amount can also be written in cents alone, with the cent sign \text{¢} after the number: 75\text{¢} is seventy-five cents, the same amount as \text{\textdollar}0.75.

As in decimal place value, the first digit after the point is tenths and the second is hundredths. With money these places have coin names, from coins and bills: a dime is 10 cents, one tenth of a dollar, and a penny is 1 cent, one hundredth of a dollar.

Intuition

The lesson is taught in three parts, one a day.

Part 1: dollars and cents as one decimal

Put an amount in a place-value chart and the money names sit right above the place names.

Figure 1Money in a place-value chart. The ones place counts dollars, the tenths place counts dimes and the hundredths place counts pennies. The rows are \text{\textdollar}4.75, \text{\textdollar}0.05 and \text{\textdollar}3.50; the gray zero fills the pennies place.

The top row is \text{\textdollar}4.75: 4 dollars, 7 dimes and 5 pennies. Seven dimes and five pennies are 70 + 5 = 75 cents, so \text{\textdollar}4.75 is 4 dollars and 75 cents. The digits after the point, read together, give the cents.

The middle row is \text{\textdollar}0.05. The 0 in the tenths place says “no dimes”, and the 5 in the hundredths place says five pennies. So 0.05 dollars is 5 cents, written 5\text{¢}. The zero right after the point is needed: without it, 0.5 would put the 5 in the dimes place, and that is 50 cents.

The bottom row is why money is written with two digits after the point, always. Three and a half dollars is 3.5 dollars, and 3.5 = 3.50, because five tenths is the same amount as fifty hundredths. But a price is written \text{\textdollar}3.50. The second digit fills the pennies place, so the number reads straight off as “three dollars and fifty cents”. A whole number of dollars may be written either way: \text{\textdollar}7 or \text{\textdollar}7.00.

To change cents to dollars, think “100 cents make a dollar”. 238 cents is 200 cents and 38 cents, so it is 2 dollars and 38 cents: \text{\textdollar}2.38. Going back, \text{\textdollar}0.68 is 68\text{¢}.

Part 2: adding, subtracting, and making change

Because money is a decimal, it adds and subtracts by the column method of adding and subtracting decimals: line up the decimal points, add or subtract each column from the right, and trade ten for one when a column needs it. With money the trades have coin names. Ten pennies make a dime, which is ten hundredths making one tenth. Ten dimes make a dollar, which is ten tenths making one, a carry across the point.

Amounts must be in the same unit before they are combined. If one price is 85\text{¢} and the other is \text{\textdollar}1.40, first write 85\text{¢} as \text{\textdollar}0.85.

Making change is a subtraction. A buyer hands over more money than the price, and the change is

\text{change} = \text{amount paid} - \text{price}.

There are two ways to find it. You can subtract in columns. Or you can count up from the price to the amount paid, the way a cashier hands back coins and bills: first pennies up to the next dime or quarter, then coins up to the next dollar, then bills. The jumps added together are the change.

Figure 2Making change from \text{\textdollar}20.00 for a price of \text{\textdollar}13.47 by counting up. The jumps are \text{\textdollar}0.03, \text{\textdollar}0.50 and \text{\textdollar}6.00, and together they make the change, \text{\textdollar}6.53. The line is not drawn to scale.

The figure counts up from a price of \text{\textdollar}13.47 to \text{\textdollar}20.00: three pennies reach \text{\textdollar}13.50, two quarters reach \text{\textdollar}14.00, and six dollars reach \text{\textdollar}20.00. The change is \text{\textdollar}0.03 + \text{\textdollar}0.50 + \text{\textdollar}6.00 = \text{\textdollar}6.53.

Part 3: several steps, budgets and estimates

Real shopping takes more than one step. Several prices are added to find a total, and the total is taken away from the money you have. A budget is the most you plan to spend; the question is whether a total fits under it, and how much is left.

Before working exactly, it helps to estimate. Round each price to the nearest whole dollar, as in rounding decimals, and add the whole numbers. Prices such as \text{\textdollar}0.99 or \text{\textdollar}4.98 are just short of a whole dollar, and friendly numbers like these make an estimate quick. The estimate tells you about how much to expect and catches a slipped decimal point.

An estimate made by rounding to the nearest dollar can come out a little above or a little below the true total. If you must be sure you have enough, round every price up to the next whole dollar. That estimate is never less than the true total, so if it fits the budget, the real total fits too.

Results

\begin{aligned} 1 \text{ dollar} &= 100 \text{ cents} \\ 1\text{¢} &= \text{\textdollar}0.01 \\ 10\text{¢} &= \text{\textdollar}0.10 \end{aligned}

An amount of some dollars and some cents, from 0 to 99 cents, is written with the dollars before the point and the cents after it as two digits. So 6 dollars and 4 cents is \text{\textdollar}6.04, and 6 dollars and 40 cents is \text{\textdollar}6.40.

Money amounts in dollars add and subtract exactly as decimals to hundredths do, with the decimal points lined up.

\begin{aligned} \text{change} &= \text{amount paid} - \text{price} \\ \text{price} + \text{change} &= \text{amount paid} \end{aligned}

Why it is true

The tenths place counts groups of \tfrac{1}{10}, and one tenth of a dollar is 100 \div 10 = 10 cents, the value of a dime. The hundredths place counts groups of \tfrac{1}{100}, and one hundredth of a dollar is 1 cent, a penny. So the digits after the point count dimes and pennies, and t dimes and h pennies are 10t + h cents: exactly the two-digit number the digits spell. That is why the two digits after the point, read together, give the cents.

Counting up gives the same answer as subtracting because subtraction finds a missing addend. If \text{price} + \text{change} = \text{paid}, then \text{change} = \text{paid} - \text{price}. Counting up builds the missing addend in pieces, and the pieces add to the whole difference.

Worked examples

Examples 1 and 2 go with Part 1, 3 to 5 with Part 2, and 6 and 7 with Part 3.

Example 1

Counting a piggy bank

Kunle’s piggy bank holds 4 one-dollar bills, 2 quarters, 2 dimes and 5 pennies. Write the total in dollars, and write the coins alone both in cents and in dollars.

Solution

The coins first, in cents. A quarter is 25 cents and a dime is 10 cents, so the coins are

2 \times 25 + 2 \times 10 + 5 = 50 + 20 + 5 = 75 \text{ cents}.

That is 75\text{¢}. Since 75 cents is 75 hundredths of a dollar, the coins are also \text{\textdollar}0.75.

With the 4 dollars from the bills, the total is 4 dollars and 75 cents. The dollars go in front of the point and the cents, as two digits, after it: \text{\textdollar}4.75.

Example 2

Reading the price stickers

Soledad is checking the garage sale stickers. A lamp is marked 3.5 dollars, a button 0.05 dollars, a mug 60\text{¢}, and a jar of coins was counted at 238 cents. Write each amount the usual way in dollars, and name the button’s price in cents. A second lamp is marked \text{\textdollar}3.05. How much more does the first lamp cost?

Solution

The lamp: 3.5 = 3.50, since five tenths is fifty hundredths. Written with two digits after the point, the price is \text{\textdollar}3.50, three dollars and fifty cents.

The button: in 0.05 the tenths digit is 0 and the hundredths digit is 5, so it is 5 pennies, 5\text{¢}. In dollars it is already written with two digits: \text{\textdollar}0.05.

The mug: 60 cents is 60 hundredths of a dollar, so 60\text{¢} = \text{\textdollar}0.60.

The jar: 238 cents is 200 cents and 38 cents, which is 2 dollars and 38 cents, \text{\textdollar}2.38.

The two lamps. \text{\textdollar}3.50 has 5 dimes; \text{\textdollar}3.05 has no dimes and 5 pennies. They are not the same price. Line up the points: hundredths 0 - 5 needs a trade, so take 1 tenth from the 5 tenths and make 10 hundredths, 10 - 5 = 5; tenths 4 - 0 = 4; ones 3 - 3 = 0.

\begin{array}{r} \text{\textdollar}3.50 \\ -\ \text{\textdollar}3.05 \\ \hline \text{\textdollar}0.45 \end{array}

The first lamp costs \text{\textdollar}0.45, or 45\text{¢}, more.

Example 3

Two items at the sale

Advika buys a lamp for \text{\textdollar}4.75 and a box of books for \text{\textdollar}2.38. What is the total?

Solution

Line up the decimal points and add each column from the right, as in adding decimals.

Pennies (hundredths): 5 + 8 = 13. Thirteen pennies are one dime and three pennies, so write 3 and carry 1 to the dimes.

Dimes (tenths): 7 + 3 + 1 = 11. Eleven dimes are one dollar and one dime, so write 1 and carry 1 across the point to the dollars.

Dollars (ones): 4 + 2 + 1 = 7.

\begin{array}{r} \text{\textdollar}4.75 \\ +\ \text{\textdollar}2.38 \\ \hline \text{\textdollar}7.13 \end{array}

The total is \text{\textdollar}7.13. As a check, \text{\textdollar}4.75 is a bit under \text{\textdollar}5 and \text{\textdollar}2.38 a bit over \text{\textdollar}2, so the total should be near \text{\textdollar}7, and it is.

Example 4

Change from a twenty

Advika’s things at the sale cost \text{\textdollar}13.47 in all. She pays with a \text{\textdollar}20 bill. Find her change by counting up, then by subtracting.

Solution

Counting up, as in the figure. Start at the price, \text{\textdollar}13.47.

Three pennies take it to \text{\textdollar}13.50, a round number of dimes: \text{\textdollar}13.47 + \text{\textdollar}0.03 = \text{\textdollar}13.50.

Two quarters take it to the next dollar: \text{\textdollar}13.50 + \text{\textdollar}0.50 = \text{\textdollar}14.00.

Six one-dollar bills take it to \text{\textdollar}20.00: \text{\textdollar}14.00 + \text{\textdollar}6.00 = \text{\textdollar}20.00.

The change is the sum of the jumps: \text{\textdollar}0.03 + \text{\textdollar}0.50 + \text{\textdollar}6.00 = \text{\textdollar}6.53.

Subtracting. Write \text{\textdollar}20 as \text{\textdollar}20.00 so it has dimes and pennies columns. The pennies column has 0 on top, and so does the dimes column, so the trade starts at the dollars: 20 dollars become 19 dollars, 9 dimes and 10 pennies, still \text{\textdollar}20.00.

Pennies: 10 - 7 = 3. Dimes: 9 - 4 = 5. Dollars: 19 - 13 = 6.

\begin{array}{r} \text{\textdollar}20.00 \\ -\ \text{\textdollar}13.47 \\ \hline \text{\textdollar}6.53 \end{array}

Both ways give \text{\textdollar}6.53. Check by adding: \text{\textdollar}6.53 + \text{\textdollar}13.47 = \text{\textdollar}20.00.

Example 5

Spending from the piggy bank

Soledad’s piggy bank holds \text{\textdollar}50.05. At the sale she buys a bike helmet for \text{\textdollar}18.69. How much does she have left? Then she buys a comic book for 85\text{¢}. How much is left now?

Solution

First, \text{\textdollar}50.05 - \text{\textdollar}18.69. Pennies: 5 is less than 9, and there are 0 dimes and 0 dollars in the ones place to trade from, so go to the tens. Take 1 ten from the 5 tens, leaving 4 tens; that ten is 10 dollars. Take 1 of those dollars, leaving 9; it is 10 dimes. Take 1 dime, leaving 9; it is 10 pennies, which joins the 5 pennies to make 15. The top number now reads 4 tens, 9 ones, 9 dimes, 15 pennies, still \text{\textdollar}50.05.

Pennies: 15 - 9 = 6. Dimes: 9 - 6 = 3. Ones: 9 - 8 = 1. Tens: 4 - 1 = 3.

\begin{array}{r} \text{\textdollar}50.05 \\ -\ \text{\textdollar}18.69 \\ \hline \text{\textdollar}31.36 \end{array}

She has \text{\textdollar}31.36 left. Check: \text{\textdollar}31.36 + \text{\textdollar}18.69 = \text{\textdollar}50.05.

The comic is priced in cents, so write it in dollars first: 85\text{¢} = \text{\textdollar}0.85. Now \text{\textdollar}31.36 - \text{\textdollar}0.85. Pennies: 6 - 5 = 1. Dimes: 3 is less than 8, so trade 1 dollar from the 1 in the ones place, leaving 0, for 10 dimes: 13 - 8 = 5. Ones: 0 - 0 = 0. Tens: 3.

\begin{array}{r} \text{\textdollar}31.36 \\ -\ \text{\textdollar}0.85 \\ \hline \text{\textdollar}30.51 \end{array}

She has \text{\textdollar}30.51 left. Check: \text{\textdollar}30.51 + \text{\textdollar}0.85 = \text{\textdollar}31.36.

Example 6

Will fifteen dollars be enough?

Kunle has \text{\textdollar}15. He picks out a puzzle for \text{\textdollar}2.89, a toy truck for \text{\textdollar}6.15, a ball for \text{\textdollar}0.99 and a board game for \text{\textdollar}4.45. Estimate the total to the nearest dollar. Can he be sure from the estimate that he has enough? Find the exact total and his change.

Solution

Round each price to the nearest whole dollar. \text{\textdollar}2.89 is nearer \text{\textdollar}3 than \text{\textdollar}2. \text{\textdollar}6.15 is nearer \text{\textdollar}6. \text{\textdollar}0.99 is one cent short of \text{\textdollar}1. \text{\textdollar}4.45 is nearer \text{\textdollar}4, since 45 cents is less than half a dollar. The estimate is

\text{\textdollar}3 + \text{\textdollar}6 + \text{\textdollar}1 + \text{\textdollar}4 = \text{\textdollar}14.

That is close to \text{\textdollar}15, and two of the prices were rounded down, so the estimate alone cannot promise the total is under \text{\textdollar}15. Rounding every price up gives \text{\textdollar}3 + \text{\textdollar}7 + \text{\textdollar}1 + \text{\textdollar}5 = \text{\textdollar}16, which is more than \text{\textdollar}15, so that check does not settle it either. The exact total is needed.

Add in steps, lining up the points each time:

\begin{aligned} \text{\textdollar}2.89 + \text{\textdollar}6.15 &= \text{\textdollar}9.04 \\ \text{\textdollar}9.04 + \text{\textdollar}0.99 &= \text{\textdollar}10.03 \\ \text{\textdollar}10.03 + \text{\textdollar}4.45 &= \text{\textdollar}14.48 \end{aligned}

In the first sum the pennies make 9 + 5 = 14 (write 4, carry a dime) and the dimes make 8 + 1 + 1 = 10 (write 0, carry a dollar), so the dollars are 2 + 6 + 1 = 9.

The total is \text{\textdollar}14.48, which is near the estimate of \text{\textdollar}14. It is less than \text{\textdollar}15, so he has enough. His change is \text{\textdollar}15.00 - \text{\textdollar}14.48 = \text{\textdollar}0.52: two pennies up to \text{\textdollar}14.50 and two quarters up to \text{\textdollar}15.00.

Example 7

Who sold what

At the end of the day the garage sale cash box holds \text{\textdollar}83.40. It started the morning with \text{\textdollar}20.00 in it, for making change. Soledad’s items brought in \text{\textdollar}21.85 and Kunle’s brought in \text{\textdollar}17.30. The rest was Advika’s. How much money did the sale take in, and how much of it was from Advika’s items?

Solution

The box holds the starting \text{\textdollar}20.00 plus everything taken in. So the sale took in

\text{\textdollar}83.40 - \text{\textdollar}20.00 = \text{\textdollar}63.40.

Soledad and Kunle together: \text{\textdollar}21.85 + \text{\textdollar}17.30. Pennies 5 + 0 = 5, dimes 8 + 3 = 11 (write 1, carry a dollar), dollars 21 + 17 + 1 = 39. That is \text{\textdollar}39.15.

Advika’s part is what remains:

\begin{array}{r} \text{\textdollar}63.40 \\ -\ \text{\textdollar}39.15 \\ \hline \text{\textdollar}24.25 \end{array}

Pennies: 0 is less than 5, so trade 1 dime for 10 pennies, 10 - 5 = 5. Dimes: 3 - 1 = 2. Dollars: 63 - 39 = 24. Advika’s items brought in \text{\textdollar}24.25.

Check by adding all three: \text{\textdollar}21.85 + \text{\textdollar}17.30 + \text{\textdollar}24.25 = \text{\textdollar}63.40. Estimate too: to the nearest dollar, 83 - 20 = 63 and 22 + 17 = 39, and 63 - 39 = 24, close to \text{\textdollar}24.25.

Boundaries

Only two places after the point. A cent is the smallest coin, so an amount paid in coins and bills stops at hundredths of a dollar. A gasoline price may show a third place, such as \text{\textdollar}3.499 for one gallon, but no one can hand over that tenth of a cent; a total is rounded to the cent before it is paid.

One sign, one unit. The dollar sign says the number counts dollars; the cent sign says it counts cents. \text{\textdollar}0.75 and 75\text{¢} are the same amount, but \text{\textdollar}75 is a hundred times more. Using both signs on one number would name two units at once, so an amount carries one sign only.

The units must match before adding. \text{\textdollar}1.40 + 85\text{¢} is not 86.40 of anything. Change the cents to dollars first, then add: \text{\textdollar}1.40 + \text{\textdollar}0.85 = \text{\textdollar}2.25.

Change is never less than zero. Making change only works when the amount paid is at least the price. If the price is more than the money on hand, the difference tells how much more is needed, not how much comes back.

Other currencies. Many countries also split their main unit into a hundred smaller ones, and their prices are written the same way. Some do not split it at all, and some split it differently, so the two-place rule belongs to the dollar and money like it, not to every currency.

Where this goes next

Buying several of the same item, such as four comic books at \text{\textdollar}1.25 each, is a repeated sum, and it leads to multiplying a decimal by a whole number. Story problems that mix bills, coins and the two signs are the work of story problems with dollars and cents. And once dollars are decimals, trading them for another country’s money is a multiplication by a rate, in currency exchange.

Exercises

Exercises 1 to 8 go with Part 1, 9 to 17 with Part 2 and 18 to 23 with Part 3. The reasoning group draws on all three.

Part 1: dollars and cents as one decimal

Write 6 dollars and 42 cents with a dollar sign.
Write 9 cents in dollars.
Kunle has 2 one-dollar bills, 3 quarters and 1 dime. Write the total in dollars.
Write \text{\textdollar}0.36 and \text{\textdollar}0.07 in cents.
Write 340 cents in dollars.
A sticker says 8.3 dollars. Write the price with two digits after the point, and say it in words.
Write \text{\textdollar}15.06 in words.
Put these prices in order from least to greatest: \text{\textdollar}2.90, \text{\textdollar}2.09, \text{\textdollar}2.19.

Part 2: adding, subtracting, and making change

Add or subtract.

\text{\textdollar}3.26 + \text{\textdollar}4.51
\text{\textdollar}5.68 + \text{\textdollar}2.79
\text{\textdollar}9.40 - \text{\textdollar}3.15
\text{\textdollar}7.05 - \text{\textdollar}2.48
A chair costs \text{\textdollar}6.82 and Advika pays with a \text{\textdollar}10 bill. Find the change by counting up.
A bike costs \text{\textdollar}14.39 and Soledad pays with a \text{\textdollar}20 bill. Find the change by subtracting, and check it by adding.
Kunle buys a pencil for 95\text{¢} and a notebook for \text{\textdollar}3.60. What is the total in dollars?
Soledad has \text{\textdollar}12.10 in her piggy bank and buys a puzzle for \text{\textdollar}7.85. How much is left?
A basket costs \text{\textdollar}3.72. The buyer pays with a \text{\textdollar}5 bill and gets back one dollar bill, one quarter and 3 pennies. Is that the right change?

Part 3: several steps, budgets and estimates

Estimate \text{\textdollar}3.79 + \text{\textdollar}1.15 + \text{\textdollar}5.62 by rounding each price to the nearest dollar, then find the exact total.
Advika’s budget is \text{\textdollar}10. She wants items costing \text{\textdollar}2.45, \text{\textdollar}3.89 and \text{\textdollar}3.20. Estimate, then find the exact total. Does it fit the budget, and how much would be left?
Soledad has \text{\textdollar}25. She buys a lamp for \text{\textdollar}8.75 and a rug for \text{\textdollar}11.60. How much does she have left?
A cash box starts with \text{\textdollar}15.00 and ends the day with \text{\textdollar}52.25. Kunle’s items brought in \text{\textdollar}19.80 of the money taken in. How much did the sale take in, and how much of that was from the other items?
Advika wants a scooter that costs \text{\textdollar}32.00. She has \text{\textdollar}18.65 in her piggy bank and earns \text{\textdollar}9.50 at the garage sale. How much more does she need?
Kunle buys two books at \text{\textdollar}1.75 each and a vase for \text{\textdollar}3.60. He pays with a \text{\textdollar}10 bill. What is his change?

Reasoning

Kunle says that \text{\textdollar}1.5 means one dollar and five cents. Use place value and coins to explain what \text{\textdollar}1.5 really means, and how it should be written.
Explain why counting up from the price to the amount paid always gives the same change as subtracting the price from the amount paid.

Answers

\text{\textdollar}6.42. The dollars go before the point and the 42 cents, as two digits, after it.
\text{\textdollar}0.09. Nine cents is nine hundredths of a dollar; the 0 after the point says no dimes.
\text{\textdollar}2.85. The coins are 3 \times 25 + 10 = 85 cents, so the total is 2 dollars and 85 cents.
36\text{¢} and 7\text{¢}. The two digits after the point are the cents: 36, and 07, which is 7.
\text{\textdollar}3.40. 340 cents is 300 cents and 40 cents, 3 dollars and 40 cents.
\text{\textdollar}8.30, eight dollars and thirty cents. 8.3 = 8.30, since three tenths is thirty hundredths.
Fifteen dollars and six cents. The digits after the point are 06: no dimes and six pennies.
\text{\textdollar}2.09, \text{\textdollar}2.19, \text{\textdollar}2.90. All have 2 dollars; compare the dimes digits, 0, 1 and 9.
\text{\textdollar}7.77. Pennies 6 + 1 = 7, dimes 2 + 5 = 7, dollars 3 + 4 = 7.
\text{\textdollar}8.47. Pennies 8 + 9 = 17, write 7 carry 1; dimes 6 + 7 + 1 = 14, write 4 carry 1; dollars 5 + 2 + 1 = 8.
\text{\textdollar}6.25. Pennies: trade a dime, 10 - 5 = 5; dimes 3 - 1 = 2; dollars 9 - 3 = 6.
\text{\textdollar}4.57. With 0 dimes, trade from the dollars: 6 dollars, 9 dimes, 15 pennies. Then 15 - 8 = 7, 9 - 4 = 5, 6 - 2 = 4. Check: \text{\textdollar}4.57 + \text{\textdollar}2.48 = \text{\textdollar}7.05.
\text{\textdollar}3.18. Three pennies to \text{\textdollar}6.85, a dime and a nickel to \text{\textdollar}7.00, three dollars to \text{\textdollar}10.00: \text{\textdollar}0.03 + \text{\textdollar}0.15 + \text{\textdollar}3.00 = \text{\textdollar}3.18.
\text{\textdollar}5.61. \text{\textdollar}20.00 is 19 dollars, 9 dimes, 10 pennies; 10 - 9 = 1, 9 - 3 = 6, 19 - 14 = 5. Check: \text{\textdollar}5.61 + \text{\textdollar}14.39 = \text{\textdollar}20.00.
\text{\textdollar}4.55. Write 95\text{¢} as \text{\textdollar}0.95; then \text{\textdollar}0.95 + \text{\textdollar}3.60 = \text{\textdollar}4.55.
\text{\textdollar}4.25. \text{\textdollar}12.10 - \text{\textdollar}7.85: trade a dime, 10 - 5 = 5; trade a dollar, 10 - 8 = 2; 11 - 7 = 4. Check: \text{\textdollar}4.25 + \text{\textdollar}7.85 = \text{\textdollar}12.10.
Yes. The change should be \text{\textdollar}5.00 - \text{\textdollar}3.72 = \text{\textdollar}1.28, and one dollar, one quarter and three pennies are \text{\textdollar}1 + \text{\textdollar}0.25 + \text{\textdollar}0.03 = \text{\textdollar}1.28.
Estimate \text{\textdollar}4 + \text{\textdollar}1 + \text{\textdollar}6 = \text{\textdollar}11. Exact: \text{\textdollar}3.79 + \text{\textdollar}1.15 = \text{\textdollar}4.94, then \text{\textdollar}4.94 + \text{\textdollar}5.62 = \text{\textdollar}10.56, close to \text{\textdollar}11.
Estimate \text{\textdollar}2 + \text{\textdollar}4 + \text{\textdollar}3 = \text{\textdollar}9. Exact: \text{\textdollar}2.45 + \text{\textdollar}3.89 = \text{\textdollar}6.34, then \text{\textdollar}6.34 + \text{\textdollar}3.20 = \text{\textdollar}9.54. It fits, with \text{\textdollar}10.00 - \text{\textdollar}9.54 = \text{\textdollar}0.46 left.
\text{\textdollar}4.65. The two items cost \text{\textdollar}8.75 + \text{\textdollar}11.60 = \text{\textdollar}20.35, and \text{\textdollar}25.00 - \text{\textdollar}20.35 = \text{\textdollar}4.65.
The sale took in \text{\textdollar}52.25 - \text{\textdollar}15.00 = \text{\textdollar}37.25. The other items brought in \text{\textdollar}37.25 - \text{\textdollar}19.80 = \text{\textdollar}17.45. Check: \text{\textdollar}17.45 + \text{\textdollar}19.80 = \text{\textdollar}37.25.
\text{\textdollar}3.85. She will have \text{\textdollar}18.65 + \text{\textdollar}9.50 = \text{\textdollar}28.15, and \text{\textdollar}32.00 - \text{\textdollar}28.15 = \text{\textdollar}3.85.
\text{\textdollar}2.90. The total is \text{\textdollar}1.75 + \text{\textdollar}1.75 + \text{\textdollar}3.60 = \text{\textdollar}7.10, and \text{\textdollar}10.00 - \text{\textdollar}7.10 = \text{\textdollar}2.90.
In 1.5 the 5 is in the tenths place, the dimes place, so \text{\textdollar}1.5 is one dollar and five dimes: 1 dollar and 50 cents. With two digits after the point it is written \text{\textdollar}1.50. One dollar and five cents has no dimes and five pennies, so it is \text{\textdollar}1.05, with a 0 in the dimes place.
The change is the amount that, added to the price, makes the amount paid. Counting up adds jumps to the price until it reaches the amount paid, so the jumps together are exactly that missing amount. Subtraction finds the same missing amount, because if \text{price} + \text{change} = \text{paid}, then \text{change} = \text{paid} - \text{price}. The jumps only split the change into easy pieces.