Multiplying
What is ½×6?
3
Interpret ¾ as a division expression. Write the division sentence that matches ¾.
¾ as division: ¾ = 3 ÷ 4
True or False: Multiplying a whole number by a fraction greater than 1 gives a product greater than the whole number. Briefly justify.
True. Multiplying by a fraction greater than 1 (e.g.,⁵⁄₄) multiplies the whole number by a value >1, producing a larger product. Multiplying by a fraction less than 1 produces a smaller product; multiplying by 1 produces the same number.
Sam shares 3 pizzas equally among 4 friends. How much pizza does each friend get? Write as a fraction.
3 pizzas shared among 4 friends: each gets 3÷4=¾ pizza
Write ⁴⁄₆ in simplest form.
⁴⁄₆ = ⅔
Find ¾×8. Show a quick model (equal groups or area) you could use.
6
(Model: 8 grouped into 4 equal parts → each part is 2; take 3 of those parts → 3×2 = 6)
Solve: If 5 whole cookies are shared equally among 8 people, how much does each person get?
Give the answer as a fraction.
5 cookies shared among 8 people: 5÷8=⅝ cookie per person
Which operation would you use and why: To find how many ⅓ cup servings are in 4 cups of juice? Then solve.
To find how many ⅓-cup servings are in 4 cups, divide by the unit fraction: 4÷⅓=4×3=12 servings.
Lina ran ⅖ of a mile each day for 5 days.
How many miles did she run in total? Use multiplication of a fraction by a whole number.
⅖×5=2 miles total
Which is larger: ⅗ or ⁴⁄₇? Explain using a strategy (common denominators, benchmarks, or models).
Compare ⅗ and ⁴⁄₇: convert to common denominator or use cross-multiplication: 3×7=21 and 4×5=20, so ⅗ is larger than ⁴⁄₇.
Multiply and simplify: ⅔ ×9.
6
Compute and explain: 7 divided by 3 as a mixed number. Show a visual or part–whole reasoning.
7 divided by 3 as a mixed number: 7÷3=2⅓
(Because 3×2=6 remainder 1 →⅓ )
Decide whether to multiply or divide and solve: You have 6 boxes. Each box contains ⅔ pound of candy. How much candy total?
Total candy: multiply (each box has ⅔ pound): 6×⅔ = 4 pounds
A container holds ¾ liter of juice. If 6 people share the juice equally, how much does each person get? Represent the problem using a visual model and compute the amount.
How many ⅔-foot pieces in 7 feet: divide by the unit fraction: 7÷⅔=7׳⁄₂=²¹⁄₂=10½ pieces.
(You can cut 10 full pieces of ⅔ foot, with a leftover piece of ⅓ foot.)
Convert 11 divided by 2 into a mixed number and as an improper fraction, and show both forms.
11 divided by 2: as an improper fraction ¹¹⁄₂; as a mixed number 5½
Compute ⅚×12 and explain whether the product is greater than, less than, or equal to 12.
10
Evaluate: ⅖ of a cake is shared equally among 3 friends. How much cake does each friend receive? (Think of dividing a fraction by a whole number.)
⅖÷3=⅖×⅓=²⁄₁₅
Each friend receives ²⁄₁₅ of the cake.
A number is multiplied by⁵⁄₄ (a fraction greater than 1). Without calculating the exact product, explain whether the result is larger or smaller than the original number and why.
Multiplying by ⁵⁄₄ (which is 1¼) makes the number larger because ⁵⁄₄ >1; the product is greater than the original number.
A baker uses ⅝ cup of sugar for one batch of cookies. He wants to make 10 batches. How much sugar is needed total? Show fraction × whole-number work and simplify.
⅝ ×10=⁵⁰⁄₈=²⁵⁄₄=6 ¼ cups of sugar
Compute: ⅞ × ⁴⁄₇ and explain why the answer makes sense.
⅞×⁴⁄₇=²⁸⁄₅₆=½ after cancellation
This makes sense because multiplying by ⁴⁄₇ removes most of the 7 and leaves half.
A recipe calls for ⅗ cup of oil for one batch. How much oil is needed for 15 batches?
Use multiplication of a fraction by a whole number and show your work.
One batch needs ⅗ cup. For 15 batches:⅗×15 ⅗×15=3 x ¹⁵⁄₅ = 3 x 3 = 9 9 cups of oil.
Solve: 9 divided by 4. Give the answer as a mixed number and explain how this shows the fraction-as-division idea ab=a÷b=ᵃ⁄b.
9 divided by 4 as a mixed number: 9÷4=2¼
As a fraction-as-division statement: ⁹⁄₄=9÷4
Determine and show work: Is 4׳⁄₂ the same as 4÷⅔? Explain using fraction-as-division and visual models.
Mr. Jones baked 8 loaves of bread. He used ⅚ of a bag of flour for each loaf. After baking, he wants to pack the remaining flour into jars that each hold ¾ of a bag.
How many full jars can he fill with the leftover flour, and how much flour (in bags) will remain unused?
Show all steps and use fraction models or equations to justify your answer.
Total flour used: 8×⅚=⁴⁰⁄₆=6 ⅔