We read your photo as:

Convert the following rational numbers to their standard form: a) -36/-63, b) -12/30, c) 24/-64

Mathematics

ScanSolve AI Answer

Answers

4 parts
a

47\frac{4}{7}

b

−25\frac{-2}{5}

c

−38\frac{-3}{8}

d

−27\frac{-2}{7}

Step-by-step solution

12 steps

Here are the rational numbers written in their standard form:

Part a· 3 steps

Given fraction: −36−63\frac{-36}{-63}

  1. Simplify the signs.

    −36−63=3663\frac{-36}{-63} = \frac{36}{63}

  2. Find the greatest common divisor (GCD) of 36 and 63.

    The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
    The factors of 63 are 1, 3, 7, 9, 21, 63.
    The GCD of 36 and 63 is 9.

  3. Divide both the numerator and the denominator by their GCD.

    36÷963÷9=47\frac{36 \div 9}{63 \div 9} = \frac{4}{7}

    The standard form is 47\boxed{\frac{4}{7}}.

Part b

−25\frac{-2}{5}

Given fraction: −1230\frac{-12}{30}

  1. The denominator is already positive.

  2. Find the GCD of 12 and 30.

    The factors of 12 are 1, 2, 3, 4, 6, 12.
    The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
    The GCD of 12 and 30 is 6.

  3. Divide both the numerator and the denominator by their GCD.

    −12÷630÷6=−25\frac{-12 \div 6}{30 \div 6} = \frac{-2}{5}

    The standard form is −25\boxed{\frac{-2}{5}}.

Part c

−38\frac{-3}{8}

Given fraction: 24−64\frac{24}{-64}

  1. Make the denominator positive by multiplying both the numerator and the denominator by -1.

    24−64=24×(−1)−64×(−1)=−2464\frac{24}{-64} = \frac{24 \times (-1)}{-64 \times (-1)} = \frac{-24}{64}

  2. Find the GCD of 24 and 64.

    The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
    The factors of 64 are 1, 2, 4, 8, 16, 32, 64.
    The GCD of 24 and 64 is 8.

  3. Divide both the numerator and the denominator by their GCD.

    −24÷864÷8=−38\frac{-24 \div 8}{64 \div 8} = \frac{-3}{8}

    The standard form is −38\boxed{\frac{-3}{8}}.

Part d

−27\frac{-2}{7}

Given fraction: −1449\frac{-14}{49}

  1. The denominator is already positive.

  2. Find the GCD of 14 and 49.

    The factors of 14 are 1, 2, 7, 14.
    The factors of 49 are 1, 7, 49.
    The GCD of 14 and 49 is 7.

  3. Divide both the numerator and the denominator by their GCD.

    −14÷749÷7=−27\frac{-14 \div 7}{49 \div 7} = \frac{-2}{7}

    The standard form is −27\boxed{\frac{-2}{7}}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QWrite each of the following rational numbers in the form of a/b, where a and b are integers and b !=…QWrite three equivalent rational numbers of: a) −7/9 b) −13/4 c) 5/3 d) −2/5 e) −3/4QAdd the following rational numbers: a) −2/5 and 4/5, b) −7/3 and 1/3, c) −11/8 and 5/8, d) −6/11 and…QExpress each of the following rational numbers in the form of a/b where a and b are integers and b…QCalculate and simplify the following expressions involving integers: a) −8 + 6, b) −12 − 20, c) 20…
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp