Sensim Math · Depth 한국어

2-2 · Four-Digit Numbers

Ten hundreds make one thousand

4.NBT.A.22.MD.C.8 · adapt · grade 4

Archetype: Place-Value Regrouping · step in a 7-type progression

▶ Practice — 12 problems

Sophie has 3 ten-dollar bills and 20 dimes. How much money does Sophie have in all?

Show solution

Understand

Sophie has 3 ten-dollar bills and 20 dimes. Find the total amount of money she has.

Givens
  • She has 3 ten-dollar bills.
  • She has 20 dimes (each dime is 10 cents).
  • Ten dimes make one dollar.
Unknowns
  • The total amount of money in all.
Constraints
  • Money is counted in dollars and cents; 100 cents make a dollar.

Plan

#8 Analyze the Units · also uses: #7 Identify Subproblems

There are two kinds of money, so I find the value of each group separately by tracking its units (bills to dollars, dimes to dollars) and then add the two totals.

Execute

#7 Identify Subproblems 2.MD.C.8
Each ten-dollar bill is worth 10,andthereare3ofthem,sothebillsareworth3times10, and there are 3 of them, so the bills are worth 3 times10, which is $30.
3×$10=$303 \times \$10 = \$30
Three tens make thirty, just like counting 10, 20, 30.
#8 Analyze the Units 2.MD.C.8
Each dime is 10 cents, and ten dimes make one dollar. So 20 dimes are 200 cents, which is $2.
20×10 cents=200 cents=$220 \times 10\text{ cents} = 200\text{ cents} = \$2
Because ten dimes equal a dollar, 20 dimes equal 2 dollars, the same way ten hundreds make a thousand.
#7 Identify Subproblems 2.MD.C.8
Combine the bills and the dimes: 30fromthebillsplus30 from the bills plus2 from the dimes is $32.
$30+$2=$32\$30 + \$2 = \$32
The total money is just the dollar amounts of each group added together.
Answer: $32

Review

The bills alone are 30andasmallpileofdimesaddsonlyacoupledollars,soatotalnear30 and a small pile of dimes adds only a couple dollars, so a total near32 is sensible; 200 cents is exactly 2,confirming2, confirming32.

Convert everything to cents: 3 bills = 3000 cents, 20 dimes = 200 cents, total 3200 cents = $32.

Standards · min grade 2

  • 2.MD.C.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies — Finding and adding the values of ten-dollar bills and dimes.
💡 Ten dimes bundle up into a dollar, so 20 dimes are just $2 to add to your bills!