Skip to learning content
← Back to Maths
Free PlanPremium View
💵
Premium UnlockedChallenge55 min

Maths • Decimal Division & Fraction Subtraction

Decimal Division and Fraction Subtraction Quest

Solve real-world decimal division and fraction subtraction problems using long division, tape diagrams, fraction bars, and regrouping models.

0

Completed

0/10

Correct

0%

Score

10

Activities

Learning Goals

  • ✓Divide decimals by whole numbers in real-world money and measurement problems.
  • ✓Use long division and place value models to explain decimal quotients.
  • ✓Subtract fractions with unlike denominators.
  • ✓Subtract mixed numbers by regrouping.
  • ✓Simplify fraction answers when possible.

Mini Lesson

  1. 1When dividing decimals by whole numbers, move the decimal point straight up into the quotient.
  2. 2Decimal division can also be shown with tape diagrams and place-value sharing.
  3. 3To subtract fractions with unlike denominators, first find a common denominator.
  4. 4When subtracting mixed numbers, regroup one whole if the fraction part on top is too small.
  5. 5Always simplify the final fraction when possible.
decimal divisionquotientdividenddivisorhundredthsunlike denominatorscommon denominatormixed numberregroupingsimplify

Interactive Activities

Tap an answer choice. The card will show feedback, the correct answer, visual model, and step-by-step explanation.

🍽️
Activity 1Decimal Division with Moneydecimal-division

Splitting the Restaurant Bill

Question

A group of 4 friends spent $62.80 on dinner. If they split the total bill evenly, how much does each person owe?

Instruction

Divide $62.80 by 4. Move the decimal point straight up into the quotient.

💡 Teacher Hint

Think: 62.80 ÷ 4. 4 goes into 62 fifteen times with money decimals continuing.

👁️ Show Visual Model: Long Division Money Model
Model Type: long-division
1 5 . 7 0
     ┌───────────
4    │ 6 2 . 8 0
      -4
      ──
       2 2
      -2 0
      ────
         2   8
        -2   8
        ──────
             0

Each person owes $15.70
✅ Show Step-by-Step Answer
  1. 1Set up 62.80 ÷ 4.
  2. 2Move the decimal point straight up into the quotient.
  3. 34 goes into 6 one time, with 2 left over.
  4. 4Bring down 2 to make 22. 4 goes into 22 five times.
  5. 5Bring down 8 tenths. 4 goes into 28 seven times.
  6. 6Bring down 0 hundredths. 4 goes into 0 zero times.
  7. 7Each person owes $15.70.
CCSS 5.NBT.B.7
🚚
Activity 2Decimal Division with Measurementdecimal-division

Fuel Tank Mileage

Question

A hybrid delivery truck drove 48.6 miles using exactly 3 gallons of gas. How many miles did the truck travel on a single gallon of gas?

Instruction

Divide the total miles by the number of gallons.

💡 Teacher Hint

48.6 ÷ 3 means split 48.6 miles into 3 equal groups.

👁️ Show Visual Model: Tape Diagram
Model Type: tape-diagram
┌──────────────────────────────────────────────┐
│                 48.6 Miles                   │
├──────────────┬──────────────┬────────────────┤
│   Gallon 1   │   Gallon 2   │    Gallon 3    │
│  16.2 miles  │  16.2 miles  │   16.2 miles   │
└──────────────┴──────────────┴────────────────┘

48.6 ÷ 3 = 16.2 miles per gallon
✅ Show Step-by-Step Answer
  1. 1The truck drove 48.6 miles.
  2. 2It used 3 gallons of gas.
  3. 3Divide 48.6 by 3.
  4. 448 ÷ 3 = 16.
  5. 50.6 ÷ 3 = 0.2.
  6. 6Combine 16 + 0.2 = 16.2.
  7. 7The truck traveled 16.2 miles per gallon.
CCSS 5.NBT.B.7
🎀
Activity 3Place Value Sharingdecimal-division

Creating Ribbon Bows

Question

An arts and crafts teacher has 14.7 meters of ribbon. She cuts the entire spool into 7 equal pieces. How long is each piece?

Instruction

Share 14 ones and 7 tenths equally among 7 groups.

💡 Teacher Hint

14 ones divided by 7 is 2 ones. 7 tenths divided by 7 is 1 tenth.

👁️ Show Visual Model: Place Value Sharing Model
Model Type: place-value-sharing
[14 Ones] shared by 7  = 2 Ones
[7 Tenths] shared by 7 = 1 Tenth

Combine:
2 + 0.1 = 2.1 meters

Each ribbon piece is 2.1 meters.
✅ Show Step-by-Step Answer
  1. 1Break 14.7 into 14 ones and 7 tenths.
  2. 2Share 14 ones into 7 equal groups.
  3. 3Each group gets 2 ones.
  4. 4Share 7 tenths into 7 equal groups.
  5. 5Each group gets 1 tenth.
  6. 6Combine 2 ones and 1 tenth.
  7. 7Each ribbon piece is 2.1 meters.
CCSS 5.NBT.B.7
🥩
Activity 4Decimal Long Divisiondecimal-division

Ground Beef Tray Packaging

Question

A grocery store butcher has 18.45 pounds of ground beef. He divides it equally into 9 identical trays. What is the exact weight of the beef on each tray?

Instruction

Divide 18.45 by 9. Keep each place value aligned.

💡 Teacher Hint

9 goes into 18 two times. Then continue past the decimal.

👁️ Show Visual Model: Long Division with Placeholder Zero
Model Type: long-division
2 . 0 5
      ┌───────────
9     │ 1 8 . 4 5
       -1 8
       ────
          0   4
             -0
             ──
              4 5
             -4 5
             ────
                0

Each tray weighs 2.05 pounds.
✅ Show Step-by-Step Answer
  1. 1Set up 18.45 ÷ 9.
  2. 2Move the decimal point straight up.
  3. 39 goes into 18 two times.
  4. 4Subtract 18 from 18 to get 0.
  5. 5Bring down 4 tenths. 9 goes into 4 zero times.
  6. 6Bring down 5 hundredths to make 45.
  7. 79 goes into 45 five times.
  8. 8Each tray weighs 2.05 pounds.
CCSS 5.NBT.B.7
🏃
Activity 5Decimal Grid Breakdowndecimal-division

Running Track Intervals

Question

Coach Adams challenges a student to run 1.25 miles by doing 5 equal sprint intervals. How long is each sprint interval?

Instruction

Think of 1.25 as 125 hundredths. Divide the hundredths by 5.

💡 Teacher Hint

125 hundredths ÷ 5 = 25 hundredths.

👁️ Show Visual Model: Decimal Grid Breakdown
Model Type: place-value-sharing
1.25 = 125 hundredths

125 hundredths ÷ 5 = 25 hundredths

25 hundredths = 0.25

Each sprint interval is 0.25 miles.
✅ Show Step-by-Step Answer
  1. 1Rewrite 1.25 as 125 hundredths.
  2. 2Divide 125 hundredths by 5.
  3. 3125 ÷ 5 = 25.
  4. 4That means 25 hundredths.
  5. 525 hundredths is written as 0.25.
  6. 6Each interval is 0.25 miles.
CCSS 5.NBT.B.7
🍋
Activity 6Subtract Fractions with Unlike Denominatorsfraction-subtraction

The Leftover Juice

Question

A large pitcher held 7/8 of a gallon of lemonade. After breakfast, 1/4 of a gallon had been drunk. How much lemonade is left?

Instruction

Change 1/4 into eighths, then subtract.

💡 Teacher Hint

1/4 is the same as 2/8.

👁️ Show Visual Model: Equivalent Fraction Bars
Model Type: fraction-bar
Start:
[ X ][ X ][ X ][ X ][ X ][ X ][ X ][   ]  = 7/8

Drunk:
[ O ][ O ][   ][   ][   ][   ][   ][   ]  = 1/4 = 2/8

Leftover:
[ X ][ X ][ X ][ X ][ X ][   ][   ][   ]  = 5/8 gallon
✅ Show Step-by-Step Answer
  1. 1Start with 7/8 gallon.
  2. 2Convert 1/4 to eighths.
  3. 31/4 = 2/8.
  4. 4Subtract 7/8 - 2/8.
  5. 5The result is 5/8 gallon.
CCSS 5.NF.A.1
🪵
Activity 7Mixed Numbers with Borrowingfraction-subtraction

Woodworking Board Length

Question

A carpenter has a wooden board measuring 5 1/3 feet long. She cuts off a piece that is 2 2/3 feet long. How long is the remaining board?

Instruction

Regroup 5 1/3 as 4 4/3, then subtract.

💡 Teacher Hint

You cannot subtract 2/3 from 1/3, so borrow 1 whole.

👁️ Show Visual Model: Mixed Number Decomposition
Model Type: fraction-bar
Original:
5 and 1/3

Regroup:
5 1/3 = 4 4/3

Subtract:
4 4/3 - 2 2/3

Wholes:
4 - 2 = 2

Fractions:
4/3 - 2/3 = 2/3

Final:
2 2/3 feet remaining
✅ Show Step-by-Step Answer
  1. 1Start with 5 1/3.
  2. 2You cannot subtract 2/3 from 1/3.
  3. 3Borrow 1 whole from 5.
  4. 45 1/3 becomes 4 4/3.
  5. 5Subtract wholes: 4 - 2 = 2.
  6. 6Subtract fractions: 4/3 - 2/3 = 2/3.
  7. 7The remaining board is 2 2/3 feet.
CCSS 5.NF.A.1
🍅
Activity 8LCD Fraction Subtractionfraction-subtraction

Garden Bed Area

Question

A tomato patch requires 4/5 of a garden bed. A pepper patch takes up 1/2 of that same garden bed. How much more space does the tomato patch use?

Instruction

Find the LCD of 5 and 2, convert both fractions to tenths, then subtract.

💡 Teacher Hint

4/5 = 8/10 and 1/2 = 5/10.

👁️ Show Visual Model: Grid LCD Method
Model Type: fraction-bar
Tomatoes:
4/5 = 8/10
[ X ][ X ][ X ][ X ][ X ][ X ][ X ][ X ][   ][   ]

Peppers:
1/2 = 5/10
[ O ][ O ][ O ][ O ][ O ][   ][   ][   ][   ][   ]

Difference:
8/10 - 5/10 = 3/10
✅ Show Step-by-Step Answer
  1. 1Find the LCD of 5 and 2.
  2. 2The LCD is 10.
  3. 3Convert 4/5 to 8/10.
  4. 4Convert 1/2 to 5/10.
  5. 5Subtract 8/10 - 5/10.
  6. 6The difference is 3/10 of a garden bed.
CCSS 5.NF.A.1
🥾
Activity 9Mixed Number Subtraction with LCDfraction-subtraction

Walking Trails

Question

Chloe planned to walk 3 3/10 miles on a nature trail. She takes a break after walking 1 4/5 miles. How much further does she need to walk?

Instruction

Convert 1 4/5 to tenths, then regroup 3 3/10 before subtracting.

💡 Teacher Hint

1 4/5 = 1 8/10. Then regroup 3 3/10 as 2 13/10.

👁️ Show Visual Model: Common Denominator and Regrouping
Model Type: fraction-bar
Step 1:
1 4/5 = 1 8/10

Step 2:
3 3/10 - 1 8/10

Step 3:
Regroup 3 3/10 as 2 13/10

Equation:
2 13/10 - 1 8/10 = 1 5/10

Simplify:
1 5/10 = 1 1/2 miles
✅ Show Step-by-Step Answer
  1. 1Convert 1 4/5 to tenths.
  2. 24/5 = 8/10, so 1 4/5 = 1 8/10.
  3. 3The problem is 3 3/10 - 1 8/10.
  4. 4You cannot subtract 8/10 from 3/10.
  5. 5Regroup 3 3/10 as 2 13/10.
  6. 6Subtract 2 13/10 - 1 8/10.
  7. 7The answer is 1 5/10.
  8. 8Simplify 1 5/10 to 1 1/2 miles.
CCSS 5.NF.A.2
🥣
Activity 10Fraction Subtraction and Simplifyingfraction-subtraction

Baking Sugar Mix-Up

Question

A mixing bowl contains 2/3 of a cup of sugar. A recipe only requires 1/6 of a cup. How much extra sugar needs to be scooped out?

Instruction

Convert 2/3 to sixths, then subtract 1/6.

💡 Teacher Hint

2/3 = 4/6. Then 4/6 - 1/6 = 3/6.

👁️ Show Visual Model: Fraction Bar Splitting
Model Type: fraction-bar
Bowl Status:
2/3 = [ ████ ][ ████ ][      ]

Slice thirds into sixths:
4/6 = [ ██ ][ ██ ][ ██ ][ ██ ][    ][    ]

Remove recipe amount:
1/6 = [ XX ][    ][    ][    ][    ][    ]

Extra sugar:
4/6 - 1/6 = 3/6 = 1/2 cup
✅ Show Step-by-Step Answer
  1. 1Start with 2/3 cup of sugar.
  2. 2The recipe needs 1/6 cup.
  3. 3Convert 2/3 to sixths.
  4. 42/3 = 4/6.
  5. 5Subtract 4/6 - 1/6.
  6. 6The result is 3/6.
  7. 7Simplify 3/6 to 1/2.
  8. 8The extra sugar is 1/2 cup.
CCSS 5.NF.A.1

Exit Ticket

What is the most important step before subtracting fractions with unlike denominators?

Show Suggested Answer

Find a common denominator so both fractions use the same-size parts before subtracting.

EthioKids Learning