Choose the THREE numbers that are equivalent to the shaded part of the model below.
Understand the Problem
The question asks to identify three numbers that are equivalent to the shaded portion of the model, which involves analyzing the fractions and decimals presented.
Answer
The equivalent numbers are $\frac{4}{5}$, $0.8$, and $\frac{16}{20}$.
Answer for screen readers
The three numbers equivalent to the shaded part are:
- $0.8$
- $\frac{16}{20}$
- $\frac{4}{5}$
Steps to Solve
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Identify the Shaded Portion Determine the fraction representing the shaded part of the model. Visually, it appears that 4 out of 5 sections are shaded, which can be represented as $\frac{4}{5}$.
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Convert $\frac{4}{5}$ to a Decimal To find the decimal equivalent, divide the numerator by the denominator: $$ \frac{4}{5} = 0.8 $$
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Check Equivalent Fractions Determine if other fractions are equivalent to $\frac{4}{5}$:
- Convert $16/20$. This fraction can be simplified: $$ \frac{16 \div 4}{20 \div 4} = \frac{4}{5} $$
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Convert Other Choices to Decimal Convert the other fractions and numbers to decimals:
- $8/20$: $$ \frac{8}{20} = 0.4 $$
- $16/20$: $$ \frac{16}{20} = 0.8 $$
- $4/5$: as calculated is $0.8$.
- $0.20$: $$ 0.20 = 0.2 $$
- $8.10$: $$ 8.10 = 8.1 $$
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Identify Matches From the above calculations, the numbers equivalent to $\frac{4}{5}$, which is $0.8$, are:
- $0.8$ (already identified)
- $\frac{16}{20}$ (equivalent)
- $\frac{4}{5}$ (equivalent)
The three numbers equivalent to the shaded part are:
- $0.8$
- $\frac{16}{20}$
- $\frac{4}{5}$
More Information
The equivalent fractions and decimals help in understanding how the same quantity can be expressed in different forms. Fractions like $\frac{16}{20}$ can simplify to $\frac{4}{5}$, providing a clearer understanding of proportions.
Tips
- Confusing the place value of decimals; for example, mistaking $0.20$ as equivalent to $0.8$.
- Not simplifying fractions fully before comparing them.
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