We read your photo as:

Verify the closure property for addition for the following pairs of rational numbers: a) 2/3 and 6, b) 1/8 and 3/4, c) -2/7 and 3/4.

Mathematics

ScanSolve AI Answer

Answers

4 parts
a

203\frac{20}{3}

b

78\frac{7}{8}

c

1328\frac{13}{28}

d

−1021-\frac{10}{21}

Step-by-step solution

8 steps

Here's how to check the closure property for addition for each pair of numbers:

The closure property for addition states that if you add any two numbers from a specific set, the result must also be in that same set. All the numbers provided are rational numbers. The set of rational numbers (Q\mathbb{Q}) is closed under addition, meaning the sum of any two rational numbers is always a rational number.

Part a· 2 steps

  1. Calculate the sum of the given rational numbers.

    The numbers are 23\frac{2}{3} and 6.

    23+6=23+183=203\frac{2}{3} + 6 = \frac{2}{3} + \frac{18}{3} = \frac{20}{3}

  2. Determine if the sum is within the set of rational numbers.

    The sum, 203\frac{20}{3}, is a rational number. Therefore, the closure property for addition holds for this pair.
    Sum: 203\boxed{\frac{20}{3}}

Part b

78\frac{7}{8}

  1. Calculate the sum of the given rational numbers.

    The numbers are 18\frac{1}{8} and 34\frac{3}{4}.

    18+34=18+68=78\frac{1}{8} + \frac{3}{4} = \frac{1}{8} + \frac{6}{8} = \frac{7}{8}

  2. Determine if the sum is within the set of rational numbers.

    The sum, 78\frac{7}{8}, is a rational number. Therefore, the closure property for addition holds for this pair.
    Sum: 78\boxed{\frac{7}{8}}

Part c

1328\frac{13}{28}

  1. Calculate the sum of the given rational numbers.

    The numbers are −27-\frac{2}{7} and 34\frac{3}{4}.

    −27+34=−828+2128=1328-\frac{2}{7} + \frac{3}{4} = -\frac{8}{28} + \frac{21}{28} = \frac{13}{28}

  2. Determine if the sum is within the set of rational numbers.

    The sum, 1328\frac{13}{28}, is a rational number. Therefore, the closure property for addition holds for this pair.
    Sum: 1328\boxed{\frac{13}{28}}

Part d

−1021-\frac{10}{21}

  1. Calculate the sum of the given rational numbers.

    The numbers are −17-\frac{1}{7} and −13-\frac{1}{3}.

    −17+(−13)=−321−721=−1021-\frac{1}{7} + \left(-\frac{1}{3}\right) = -\frac{3}{21} - \frac{7}{21} = -\frac{10}{21}

  2. Determine if the sum is within the set of rational numbers.

    The sum, −1021-\frac{10}{21}, is a rational number. Therefore, the closure property for addition holds for this pair.
    Sum: −1021\boxed{-\frac{10}{21}}

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

QAdd 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…QProve that the following rational numbers are equal: 2/3 and 4/6 (iii) −3/5 and −6/10 Find the sum…QWrite three equivalent rational numbers of: a) −7/9 b) −13/4 c) 5/3 d) −2/5 e) −3/4QCalculate the sum and difference of these fractions: 3/4 + (−4/3) + 5/6, and verify if it equals…
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