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Write 10 and one-third minus three-eighths in its simplest form.
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10 and one-third is a mixed number and three-eighth is a fraction.
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To subtract a fraction from a mixed number, we’ll need to find a common denominator.
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What would be the least common multiple between three and eight?
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Three times eight equals 24, and that means 24 is a multiple of three and eight.
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Three times eight equals 24.
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If we multiply the denominator by eight, we need to multiply the numerator by eight.
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One times eight equals eight.
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Eight times three equals 24.
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If we multiply the denominator on this side by three, we need to multiply the numerator by three.
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Three times three equals nine.
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Now we have common denominators, we see that we’re trying to subtract nine twenty-fourths from 10 and eight twenty-fourths.
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However, we can’t subtract nine from eight.
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And that means we need to borrow from our whole number.
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Instead of having 10, we can separate that 10 into nine plus one plus eight twenty-fourths.
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And we wanna turn that one into a value with a denominator of 24.
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Twenty-four twenty-fourths is the same thing as one.
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Now we can add 24 plus eight, which equals 32.
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The denominator stays the same; it stays 24.
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And our whole number is now nine.
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Nine and thirty-two twenty-fourths is the same thing as 10 and one-third.
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And we’re going to subtract nine twenty-fourths.
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To do this we’ll subtract the numerators, 32 minus nine equals 23.
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The denominator doesn’t change; it’s still four.
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And we’re not subtracting anything from our whole number.
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So it stays nine.
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23 is a prime number, and that means the fraction twenty-three twenty-fourths is in its simplest form: nine and twenty-three twenty-fourths.