Combined Operations: Solved Exercises

First, we solve the multiplication

Then we substract

First, we solve the division

Then we substract

First, we solve the multiplication

Then we add and subtract

First, we solve the multiplication

Then we subtract

First, we solve the division

Then we substract

First, we solve the multiplication

Then we add and subtract

First, we solve the division

Then we add and subtract

First, we solve the multiplications and divisions

Then we add and subtract

We start by solving the multiplications inside the parentheses

Then we perform the addition inside the parentheses and multiply the results

First, we solve the multiplications and divisions

We perform the addition and subtraction inside the parentheses, and then add the resulting values

First, we solve the multiplications inside the parentheses and calculate the exponent

Then we perform the multiplication and add the results

First, we solve the subtraction inside the parentheses



Then we perform the multiplication and add the results

First, we solve the multiplications, then the additions inside the parentheses



We carry out the multiplications and then the additions inside the parentheses

We solve the operations inside the innermost parentheses, keeping in mind the following: first, we perform multiplications and divisions, then additions and subtractions to simplify the results. If there are still parentheses remaining, we repeat the process.

We remove the parentheses. Since the second one has a minus sign in front, we take the opposite — meaning we change the signs of all the terms inside

First, we perform the addition inside the parentheses, then divide the fractions, and finally simplify

We solve the operations inside the parentheses, multiply the results, and simplify

We solve the operations inside the parentheses, divide the results, and simplify

We remove the inner parentheses by first doing the multiplications and divisions, then the additions and subtractions. We repeat this process until no parentheses remain.

We remove the inner parentheses by first doing the multiplications and divisions, then the additions and subtractions. We repeat this process until no parentheses remain.

We write the expression as a division of two fractions

We solve the operations in the numerator

The resulting fraction is written as a division of two fractions — we simplify, perform the division, and simplify again

We solve the operations in the denominator

The resulting fraction is written as a division of two fractions — we perform the division and simplify again

We solve the operations in the numerator and denominator

The resulting fraction is written as a division of two fractions — we simplify, perform the division, and simplify again

We solve the operations in the numerator and denominator

The resulting fraction is written as a division of two fractions — we simplify, perform the division, and simplify again

First, we solve

Then, we take the reciprocal:

1 We solve the operations inside the parentheses. In the second denominator, we multiply first, then divide

2 is a mixed number, so we keep the denominator (7) and the numerator is the product of the whole number (5) and the denominator (7) plus the numerator of the fraction (1).

3 We solve the operations and simplify

4 We solve the operations and reduce to a common denominator in the second fraction

5 We evaluate the exponents. When a fraction is raised to a negative exponent, we swap the numerator and denominator before applying the exponent

1 We solve the expressions inside both sets of parentheses

2 After removing the inner parentheses, the bracket becomes a parenthesis

3 We perform the division and multiplication inside the parentheses and simplify the results

4 We divide by the result of the parentheses and simplify

1 We reduce the fractions inside each parenthesis to a common denominator. We also convert the mixed number to an improper fraction by keeping the denominator (2) and adding the product of the whole number (2) and the denominator (2) to the numerator (1).

2 We perform the operations in the numerators. In the second bracket, after removing parentheses, we replace it with a parenthesis

3 We evaluate the exponent. Since there are no more parentheses in the first bracket, we replace it with a parenthesis

4 We multiply in the first parenthesis and divide in the second

5 We add the fractions in the first parenthesis, simplify the second, and then divide

1 First, we work with the products and mixed numbers inside the parentheses.

2 We solve the expressions inside the parentheses and simplify

3 We perform the multiplication and simplify; we replace the bracket with a parenthesis

4 We perform the operations inside the parenthesis