Find the value of t in this pair of equivalent fractions: 7/8 = t/32
Understand the Problem
The question is asking us to find the value of t in the equivalent fractions 7/8 and t/32. We need to set up a proportion and solve for t.
Answer
The value of $t$ is $28$.
Answer for screen readers
The value of $t$ is $28$.
Steps to Solve
- Set up the proportion
We start with the equation given in the problem:
$$ \frac{7}{8} = \frac{t}{32} $$
- Cross-multiply
To solve for $t$, we will cross-multiply. This means we multiply the numerator of one fraction by the denominator of the other fraction:
$$ 7 \times 32 = 8 \times t $$
- Calculate the multiplication
Calculating the left side gives:
$$ 7 \times 32 = 224 $$
Now we have:
$$ 224 = 8t $$
- Isolate $t$
To find $t$, divide both sides of the equation by 8:
$$ t = \frac{224}{8} $$
- Simplify the division
Calculating the right side:
$$ t = 28 $$
The value of $t$ is $28$.
More Information
The method used here is based on the property of equivalent fractions. Since two fractions are equal, their cross products must also be equal. This technique is commonly used in solving for unknowns in proportions.
Tips
- Forgetting to cross-multiply correctly.
- Incorrectly simplifying after dividing.
- Mixing up the values while setting the proportion.
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