What's [tex]$6 / 7$[/tex] written as a fraction with a denominator of 42?
A) [tex]$6 / 42$[/tex]
B) [tex]$42 / 42$[/tex]
C) [tex]$36 / 42$[/tex]
D) [tex]$7 / 42$[/tex]
Answer (2)
Determine the multiplier by dividing the target denominator by the original denominator: 42/7 = 6 .
Multiply both the numerator and denominator of the original fraction by the multiplier: 7 × 6 6 × 6 .
Calculate the new numerator: 6 × 6 = 36 .
The equivalent fraction is 42 36 .
Explanation
Understanding the Problem We need to express the fraction 7 6 as an equivalent fraction with a denominator of 42 . This means we need to find a number that we can multiply both the numerator and the denominator of 7 6 by, such that the new denominator is 42 .
Finding the Multiplier To find the multiplier, we divide the desired denominator ( 42 ) by the current denominator ( 7 ). So, we calculate 42 ÷ 7 = 6 . This means we need to multiply both the numerator and the denominator of 7 6 by 6 .
Calculating the Equivalent Fraction Now, we multiply the numerator and the denominator of 7 6 by 6 :
7 × 6 6 × 6 = 42 36 So, the equivalent fraction is 42 36 .
Identifying the Correct Option Comparing our result with the given options, we see that 42 36 matches option C.
Final Answer Therefore, 7 6 written as a fraction with a denominator of 42 is 42 36 .
Examples
Imagine you are baking a cake and the recipe calls for 7 6 of a cup of flour. However, your measuring cups are only marked in 42 nds of a cup. To find out how many 42 nds of a cup you need, you would convert 7 6 to an equivalent fraction with a denominator of 42 . This conversion helps you measure the correct amount of flour, ensuring your cake turns out perfectly.
The fraction 7 6 can be rewritten with a denominator of 42 as 42 36 . This is done by finding a multiplier of 6 and applying it to both the numerator and the denominator. Therefore, the correct answer is option C.
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