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Solve Multi-Step Problems Using Decimal Operations

Students apply all four decimal operations to solve multi-step real-world and mathematical problems. They select appropriate operations, estimate to check reasonableness, and clearly communicate their solution process.

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Solve Multi-Step Problems Using Decimal Operations

Grade 5 · Decimal Operations · question 1 of 3

0 of 20

20 rungs. A star at the top.

Ivy buys 4 erasers at $0.80 each and pays with a $5.00 bill. How much change should she get?

How it is taught

0:00 of 4:36

A multi-step decimal problem needs more than one operation.

You estimate, then compute, so you can tell if the answer is reasonable.

Read it: Decimal stories in two steps

Ana buys 4 pens at $1.35 each and pays with $10. First step: 4 × $1.35 = $5.40. Carry $5.40 down: $10.00 − $5.40 = $4.60 in change.

  1. Read the story and find the two jobs, in order.
  2. Do the first job, and write its answer with its $ or its unit.
  3. Carry that answer into the second job: the last answer is the story's answer.

The pens cost 4 × $1.35, so that is what comes out of the $10.

Money is written to the cent: $5.40, not $5.4.

Each answer is used once, in the next step, so no number is left out.

Two steps in the story's order, each answer carried into the next.

Stopping at the first answer: $5.40 is what the pens cost, not the change.

Carry it down: $10.00 − $5.40 = $4.60.

Mia buys 5 notebooks at $1.25 each and pays with $10.00. How much change does she get? $___ — 3.75. 5 × $1.25 = $6.25, then $10.00 − $6.25 = $3.75.

3 notebooks at $2.45 each, paid with $10 — how much change?

Maya buys three notebooks. Each notebook costs two dollars and forty-five cents. She pays with a ten-dollar bill. How much change does she get back?

This problem has two steps. First we'll find the total cost. Then we'll subtract from ten dollars to find the change.

Step one: multiply two-point-four-five by three to get the total cost.

Three times two-point-four-five equals seven dollars and thirty-five cents. Keep the decimal point lined up.

Let's check. Two-point-four-five rounds to two-point-five, and three times two-point-five is seven-point-five. Our answer of seven-point-three-five is very close, so it makes sense.

3 notebooks · $2.45 each · paid $10How much change does Maya get?Plan: 2 steps1. Total cost = 3 × $2.452. Change = $10 − totalStep 1: Total cost$2.45×3$7.35Check ≈$2.45 ≈ $2.503 × $2.50 = $7.50$7.35 is close ✓Step 2: Change$10.00−$7.35$2.65$10 − $7 ≈ $3$2.65 fits ✓Plan → Compute → CheckMultiply, then subtract — line up decimals!CHANGE$2.65Maya's change
Grade 5 · Plan, compute, and check with decimals

Step two: subtract the cost from ten dollars. Line up the decimal points carefully.

Ten minus seven-point-three-five equals two dollars and sixty-five cents.

Quick check: ten minus seven is three, and our answer is just under three. That fits!

Maya gets two dollars and sixty-five cents in change. When problems have many steps, plan first, compute carefully, and check that your answer is reasonable.

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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