Multiplying a fraction by a whole number means taking that fraction repeatedly a certain number of times. For example, 14×3\frac{1}{4}\times 341​×3 means “3 groups of one‑quarter.”

Quick Scoop

  • Turn the whole number into a fraction (put it over 1).
  • Multiply the top numbers (numerators).
  • Multiply the bottom numbers (denominators).
  • Simplify the fraction if possible.

Step‑by‑Step Method

  1. Rewrite the whole number as a fraction
    • Example: 5=515=\frac{5}{1}5=15​.
  1. Multiply the numerators (top numbers)
    • Example: 23×5=23×51⇒2×5=10\frac{2}{3}\times 5=\frac{2}{3}\times \frac{5}{1}\Rightarrow 2\times 5=1032​×5=32​×15​⇒2×5=10.
  1. Multiply the denominators (bottom numbers)
    • Using the same example: 3×1=33\times 1=33×1=3, so you get 103\frac{10}{3}310​.
  1. Simplify or turn into a mixed number if needed
    • 103=313\frac{10}{3}=3\frac{1}{3}310​=331​.

Worked Examples

Think of it as “repeated addition,” but much quicker.

Example 1: 18×5\frac{1}{8}\times 581​×5

  • Step 1: 5=515=\frac{5}{1}5=15​.
  • Step 2: Multiply numerators: 1×5=51\times 5=51×5=5.
  • Step 3: Multiply denominators: 8×1=88\times 1=88×1=8.
  • Answer: 58\frac{5}{8}85​.

Example 2: 34×4\frac{3}{4}\times 443​×4

  • Step 1: 4=414=\frac{4}{1}4=14​.
  • Step 2: Numerators: 3×4=123\times 4=123×4=12.
  • Step 3: Denominators: 4×1=44\times 1=44×1=4.
  • Step 4: 124=3\frac{12}{4}=3412​=3.

Visual / Real‑Life Picture

  • 13×15\frac{1}{3}\times 1531​×15 can be seen as “one‑third of 15.”
  • You can imagine 15 objects split equally into 3 groups; each group has 5, so 13×15=5\frac{1}{3}\times 15=531​×15=5.

Tiny Story to Remember It

Imagine you have a recipe that uses 25\frac{2}{5}52​ of a cup of sugar for one batch of cookies, and you want to bake 3 batches.

  • You are really doing 25×3\frac{2}{5}\times 352​×3: three groups of 25\frac{2}{5}52​.
  • Convert 3 to a fraction: 31\frac{3}{1}13​.
  • Multiply: 25×31=65=115\frac{2}{5}\times \frac{3}{1}=\frac{6}{5}=1\frac{1}{5}52​×13​=56​=151​ cups of sugar total.

Quick HTML Table: Examples

html

<table>
  <tr>
    <th>Expression</th>
    <th>Step Form</th>
    <th>Answer</th>
  </tr>
  <tr>
    <td>1/8 × 5</td>
    <td>(1/8) × (5/1)</td>
    <td>5/8</td>
  </tr>
  <tr>
    <td>3/4 × 4</td>
    <td>(3/4) × (4/1)</td>
    <td>3</td>
  </tr>
  <tr>
    <td>2/5 × 3</td>
    <td>(2/5) × (3/1)</td>
    <td>6/5 = 1 1/5</td>
  </tr>
</table>

Tiny TL;DR

To multiply fractions with whole numbers, write the whole number over 1, multiply tops, multiply bottoms, then simplify.

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