Arithmetic - SAT Math

The terms shown are complex fractions. We first need to simplify each and find the least common denominator before solving.

Rewrite the complex fraction using a division sign.

Change the division sign to a multiplication sign, and take the reciprocal of the second term.

Repeat this step for the second term.

Add the two terms together.

The answer is:

Add what he can purchase to what he has left over:

Two comic books and the candy bar: $1.50 + $1.0 + $0.75 = $3.75

Three quarters and two dimes: $0.75 + $0.20 = $0.95

Therefore his total amount of money is $3.75 + $0.95 = $4.70.

In order to add the decimals, add placeholders to the decimal .

Be careful not to add the wrong digits!

Add the thousandths places.

Add the hundredths places.

Add the tenths places.

Combine the numbers and put a decimal before the tenths place.

The correct answer is:

There are three routes from Point A to Point B, and three from Point B to Point C, for a total of routes total. The total distance traveled is the distance of one of the first three routes added to that of one of the last three; we can take all nine possibilities and add the distances:

Five of these routes require driving a distance 40 miles or fewer.

Each route includes one path from Point A to Point B and one path from Point B o Point C.

The shortest possible drive is the sum of the shortest paths for each leg of the trip:

The longest possible drive is the sum of the longest paths for each leg of the trip:

The correct response is that .

The family's trip will be designed so that the family will take two different routes of the three that connect Town A and Town B, and two different routes of the three that connect Town B and Town C.

The minimum distance that the family will travel is therefore the sum of the lengths of the two shortest routes from Town A to Town B, and those of the two shortest routes from Town B to Town C:

miles

The maximum distance that the family will travel is, similarly, the sum of the lengths of the two longest routes from Town A to Town B, and those of the two longest routes from Town B to Town C:

miles

The correct choice is therefore .

Pick any even integer (2, 4, 6, etc.) to represent x. The only value that is odd is 3_x_ + 1. Any number multiplied by an even integer will be even. When an even number is added and subtracted to that product, the result will be even as well. 3_x_ + 1 is the only choice that adds an odd number to the product.

Add the ones digit.

Since the number is 10 or greater, the tens digit is the carryover.

Add the tens digit with the carryover.

Add the hundreds digit with the carryover.

Combine all the ones digits in our calculations.

The answer is .

1/3 of the movies are action movies. 3/5 of 2/3 of the movies are comedies, or (3/5)*(2/3), or 6/15. Combining the comedies and the action movies (1/3 or 5/15), we get 11/15 of the movies being either action or comedy. Thus, 4/15 of the movies remain and all of them have to be historical.

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

Substitute the values of x and y into the given expression:

2(1/3) + 3(1/2)

= 2/3 + 3/2

= 4/6 + 9/6

= 13/6

Finding the common denominator yields . We can then evaluate leaving .

Find the least common denominator to solve this problem

Multiply 27 with , and multiply with 3 to obtain common denominators.

Convert the fractions.

Combine the terms as one fraction.

The answer is:

Terms are obtained by alternately adding 5 and multiplying by 3:

The missing two elements are found by multiplying by 3, then by adding 5:

Multiplying by 3 confirms that this is correct:

In the word we have 4 vowels (3 x 4 = 12 points) and 6 consonants (5 x 6= 30). If we add the points together we get a total of 42 points.

Listing them all, 10-20-30-40-50-60-70-80-90-100-110-120-130-140 you see you can divide the numbers in half (7 pairs). Alternatively you can take (140-10+10)/2/10, adding that additional +10 in the numerator because it is inclusive, giving you 7. Just adding the top and bottom numbers gives you 10+140 for 150. 150*7 is 1050.

After the first term, the next four terms are obtained by adding, multiplying, subtracting, and dividing by 2, in order. The four terms after that are obtained by carrying out the same operations with 4. The next term is obtained by adding 6, so the operations can be expected to be repeated with 6, the next even number.

Observe the operations as carried out with 2:

Carrying out the same steps, in order, with 4:

Carrying out the same steps, in order, with 6:

, the number that replaces the circle;

, the number that replaces the square.