3.3-multiplication and division with mixed numbers math 081 catherine conway

3.3-Multiplication and Division with Mixed Numbers

MATH 081

CATHERINE CONWAY

Steps to multiply or divide mixed numbers 1. Convert all mixed numbers into improper fractions

2. For Multiplication ◦ multiply the numerators◦ multiply the denominators◦ Simplify (Reduce fraction to lowest terms)

3. For Division◦ Keep, change, flip◦ Follow the step 2

NOTE: Always following the order of operation when necessary and fractions should always be reduced to lowest terms.

Examples - Multiply𝟐𝟏𝟑∙𝟔

𝟑𝟒 Convert to improper fractions

𝟕𝟑∙𝟐𝟕𝟒

Multiply numerator Multiply denominators

𝟏𝟖𝟗𝟏𝟐

Reduce the fraction and change into mixed number

𝟏𝟓𝟑𝟒

Cross cancel𝟕𝟏∙𝟗𝟒

𝟔𝟑𝟒

𝟔𝟑𝟒

=¿ 𝟏𝟓𝟑𝟒

Examples - Multiply𝟏𝟎 ∙𝟏

𝟏𝟒 Convert to improper fractions

𝟏𝟎𝟏∙𝟓𝟒


𝟓𝟎𝟒


𝟏𝟐𝟏𝟐

Cross cancel𝟓𝟏∙𝟓𝟐

𝟐𝟓𝟐

𝟐𝟓𝟐

=¿ 𝟏𝟐𝟏𝟐

Examples - Multiply𝟑𝟏𝟓∙𝟓

𝟏𝟔∙𝟏

𝟏𝟖

Convert to improper fractions

𝟏𝟔𝟓∙𝟑𝟏𝟔∙𝟗𝟖


𝟒𝟒𝟔𝟒𝟐𝟒𝟎


𝟏𝟖𝟑𝟓

Cross cancel

𝟗𝟑𝟓

𝟗𝟑𝟓

=¿ 𝟏𝟖𝟑𝟓

𝟐𝟓∙𝟑𝟏𝟐∙𝟑𝟏

=¿𝟏𝟓∙𝟑𝟏𝟏∙𝟑𝟏

Examples - DivideConvert to improper fractions 𝟗

𝟓÷𝟏𝟕𝟔


𝟓𝟒𝟖𝟓

Reduce the fraction and change into mixed number (if possible)

𝟏𝟒𝟓÷𝟐

𝟓𝟔

Keep, Change, Flip 𝟗𝟓∙𝟔𝟏𝟕

𝟓𝟒𝟖𝟓

Examples - DivideConvert to improper fractions 𝟏𝟐

𝟏÷𝟏𝟗𝟔


𝟕𝟐𝟏𝟗

Reduce the fraction and change into mixed number (if possible)

𝟏𝟐÷𝟑𝟏𝟔

Keep, Change, Flip 𝟏𝟐𝟏∙𝟔𝟏𝟗

𝟑𝟏𝟓𝟏𝟗

Examples - DivideConvert to improper fractions


Change into mixed number

𝟕𝟖÷(𝟏𝟏𝟒 ÷𝟒)

Order of operationsKeep, Change, Flip

𝟕𝟖÷(𝟓𝟒 ÷ 𝟒𝟏 )

𝟕𝟖÷(𝟓𝟒 ∙𝟏𝟒 )𝟕𝟖÷( 𝟓𝟏𝟔 )

Keep, Change, Flip 𝟕𝟖∙𝟏𝟔𝟓

Cross Cancel


𝟕𝟏∙𝟐𝟓

𝟏𝟒𝟓

𝟐𝟒𝟓

Examples - Divide

Convert to improper fractions


Change into mixed number

𝟒 𝟑𝟓∙(𝟐 𝟏

𝟒÷𝟓)

Order of operationsKeep, Change, Flip

𝟐𝟑𝟓∙(𝟗𝟒 ÷𝟓𝟏 )

𝟐𝟑𝟓∙(𝟗𝟒 ∙𝟏𝟓 )

𝟐𝟑𝟓∙( 𝟗𝟐𝟎 )


𝟐𝟎𝟕𝟏𝟎𝟎

𝟐𝟕

𝟏𝟎𝟎

3.3-multiplication and division with mixed numbers math 081 catherine conway

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