A model may help you understand multiplication of fractions. We will use fraction tiles to model [latex]\frac{1}{2}\cdot \frac{3}{4}[/latex].
To multiply [latex]\frac{1}{2}[/latex] and [latex]\frac{3}{4}[/latex], think “I need to find [latex]\frac{1}{2}[/latex] of [latex]\frac{3}{4}[/latex].”
Start with fraction tiles for three-fourths. To find one-half of three-fourths, we need to divide them into two equal groups. Since we cannot divide the three [latex]\frac{1}{4}[/latex] tiles evenly into two parts, we exchange them for smaller tiles.
A rectangle is divided vertically into three equal pieces. Each piece is labeled as one fourth. There is a an arrow pointing to an identical rectangle divided vertically into six equal pieces. Each piece is labeled as one eighth. There are braces showing that three of these rectangles represent three eighths.
We see [latex]\frac{6}{8}[/latex] is equivalent to [latex]\frac{3}{4}[/latex]. Taking half of the six [latex]\frac{1}{8}[/latex] tiles gives us three [latex]\frac{1}{8}[/latex] tiles, which is [latex]\frac{3}{8}[/latex].
Use a diagram to model [latex]\frac{1}{3}\cdot \frac{2}{5}[/latex]
Solution:
You want to find one-third of two-fifths.
First shade in [latex]\frac{2}{5}[/latex] of the rectangle.
A long rectangle is divided into five equal sections with vertical lines. Two of the resulting boxes are shaded blue.
We will take [latex]\frac{1}{3}[/latex] of this [latex]\frac{2}{5}[/latex], so we heavily shade [latex]\frac{1}{3}[/latex] of the shaded region.
A long rectangle is divided into five equal sections with vertical lines and three equal sections with horizontal lines. There are fifteen resulting boxes and two are shaded dark blue to show the overlap.
Notice that [latex]2[/latex] out of the [latex]15[/latex] pieces are heavily shaded. This means that [latex]\frac{2}{15}[/latex] of the rectangle is heavily shaded.
Therefore, [latex]\frac{1}{3}[/latex] of [latex]\frac{2}{15}[/latex] is [latex]\frac{2}{15}[/latex], or [latex]\frac{1}{3}\cdot \frac{2}{5}=\frac{2}{15}[/latex]
Answers & Comments
Answer:
Fraction Multiplication
A model may help you understand multiplication of fractions. We will use fraction tiles to model [latex]\frac{1}{2}\cdot \frac{3}{4}[/latex].
To multiply [latex]\frac{1}{2}[/latex] and [latex]\frac{3}{4}[/latex], think “I need to find [latex]\frac{1}{2}[/latex] of [latex]\frac{3}{4}[/latex].”
Start with fraction tiles for three-fourths. To find one-half of three-fourths, we need to divide them into two equal groups. Since we cannot divide the three [latex]\frac{1}{4}[/latex] tiles evenly into two parts, we exchange them for smaller tiles.
A rectangle is divided vertically into three equal pieces. Each piece is labeled as one fourth. There is a an arrow pointing to an identical rectangle divided vertically into six equal pieces. Each piece is labeled as one eighth. There are braces showing that three of these rectangles represent three eighths.
We see [latex]\frac{6}{8}[/latex] is equivalent to [latex]\frac{3}{4}[/latex]. Taking half of the six [latex]\frac{1}{8}[/latex] tiles gives us three [latex]\frac{1}{8}[/latex] tiles, which is [latex]\frac{3}{8}[/latex].
Therefore, [latex]\frac{1}{2}\cdot \frac{3}{4}=\frac{3}{8}[/latex]
EXAMPLE
Use a diagram to model [latex]\frac{1}{3}\cdot \frac{2}{5}[/latex]
Solution:
You want to find one-third of two-fifths.
First shade in [latex]\frac{2}{5}[/latex] of the rectangle.
A long rectangle is divided into five equal sections with vertical lines. Two of the resulting boxes are shaded blue.
We will take [latex]\frac{1}{3}[/latex] of this [latex]\frac{2}{5}[/latex], so we heavily shade [latex]\frac{1}{3}[/latex] of the shaded region.
A long rectangle is divided into five equal sections with vertical lines and three equal sections with horizontal lines. There are fifteen resulting boxes and two are shaded dark blue to show the overlap.
Notice that [latex]2[/latex] out of the [latex]15[/latex] pieces are heavily shaded. This means that [latex]\frac{2}{15}[/latex] of the rectangle is heavily shaded.
Therefore, [latex]\frac{1}{3}[/latex] of [latex]\frac{2}{15}[/latex] is [latex]\frac{2}{15}[/latex], or [latex]\frac{1}{3}\cdot \frac{2}{5}=\frac{2}{15}[/latex]
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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