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The area of a rectangle is found by multiplying length by width, so 8 × 5 = 40 square centimeters. Adding the two sides (13) gives only half the perimeter, and 26 is the full perimeter, not the area.
Dividing the numerator by the denominator, 3 ÷ 4 = 0.75, so 3/4 equals 0.75. The digits of the fraction cannot simply be copied into decimal places.
Rounding to the nearest hundred keeps 500 for any number from 450 through 549. The number 463 lies inside that range, so it rounds to 500.
Compare tenths first: 0.06 has zero tenths, so it is smallest. Then 0.6 has six tenths and 0.66 has six tenths plus six hundredths, so the order is 0.06, 0.6, 0.66.
A square has four equal sides, so the perimeter is 4 × 9 = 36 inches. The value 81 is the area, found by multiplying a side by itself.
Multiplying the numerator and denominator of 2/3 by the same number 2 gives 4/6, so the two fractions name the same amount. Equivalent fractions must be made by multiplying or dividing both parts by the same nonzero number.
Rounding 19 to 20 and multiplying by 4 gives about 80 centimeters, a reasonable estimate. Exact multiplication gives 76, which is closest to 80.
A number with remainder 4 when divided by 6 equals a multiple of 6 plus 4. Since 18 is a multiple of 6, 18 + 4 = 22 gives remainder 4.
Each term increases by 4, since 7 − 3 = 4 and 11 − 7 = 4. Adding 4 to 15 gives 19 as the next term.
The perimeter of a rectangle is 2 × (length + width), so 2 × (12 + 7) = 2 × 19 = 38 meters. The value 84 is the area, found by multiplying length by width.
Rewrite 3/4 as 6/8 so both fractions have the same denominator. Since 5/8 is less than 6/8, the true statement is 5/8 < 3/4.
First find the total muffins: 8 × 12 = 96. Then divide by 6 per box: 96 ÷ 6 = 16 boxes.
Place value builds the number from left to right: 4 thousands is 4,000, 0 hundreds adds nothing, 7 tens is 70, and 2 ones is 2. Combined, that is 4,072.
Since area equals length times width, the length is the area divided by the width: 48 ÷ 6 = 8 inches.
A straight angle measures 180 degrees, so the two parts must add to 180. Subtracting gives 180 − 65 = 115 degrees.
Work backward: subtract 5 from 40 to get 35, then divide by 7 to get 5. Checking, 5 × 7 + 5 = 40 confirms the answer.
There are 10 marbles in all, and blue has the most marbles (5), so blue has the greatest probability. The chance of blue is 5/10, which is larger than 3/10 for red and 2/10 for green.
A multiple of both 4 and 6 must be divisible by each. Since 24 ÷ 4 = 6 and 24 ÷ 6 = 4, the number 24 works.
First multiply 15 × 6 = 90 pages for the first six days. Then add the seventh day: 90 + 22 = 112 pages.
The decimal 0.4 means four tenths, which is 4/10. To change a decimal to a percent, multiply by 100, so 0.4 = 40%.
Find each rectangle's area and add: 5 × 3 = 15 and 4 × 3 = 12, so 15 + 12 = 27 square units.
Numbers from 3,550 through 3,649 round to 3,600. The number 3,551 falls inside that range, so it rounds to 3,600.
The pattern repeats every 3 shapes. Dividing 23 by 3 gives 7 full groups with remainder 2, so the 23rd shape is the second shape in the group, which is a square.
The pool area is 15 × 8 = 120 square meters. Adding 1 meter on each side makes the outer rectangle 17 by 10, with area 170. The walkway area is 170 − 120 = 50 square meters.
A sum of 1 means the two fractions are complementary parts of a whole, so the missing part is 8/8 − 3/8 = 5/8. Adding 3/8 + 5/8 = 8/8 = 1 confirms it.
In 5,082 the digits from left to right are 5 thousands, 0 hundreds, 8 tens, and 2 ones. The 8 sits in the tens place, so its value is 8 × 10 = 80. The place of a digit, not the digit itself, decides its value.
Four hundred six thousand gives 406 in the thousands period, and thirty-two gives 032 in the ones period. Joining the periods gives 406,032. Each period holds exactly three digits, so the zero in the hundreds place of the thousands period must be written.
Multiply 3 1/4 by 2/3. First change 3 1/4 to 13/4, then multiply: 13/4 × 2/3 = 26/12 = 13/6 = 2 1/6. The answer is less than 3 1/4, which makes sense because only part of the trail was covered.
Multiply 3/4 by 5: 3/4 × 5 = 15/4. Rewriting 15/4 as a mixed number gives 3 3/4 cups. The answer is a little less than 4 cups, which matches 5 groups slightly smaller than 1 cup each.
Multiply 24 by 15. Using partial products: 24 × 10 = 240 and 24 × 5 = 120, and 240 + 120 = 360. So the theater has 360 seats.
Divide 372 by 6. Since 6 × 60 = 360 and 12 remain, and 6 × 2 = 12, the quotient is 62. Checking by multiplication, 62 × 6 = 372, confirms the answer.
The phrase 4 times as many as 7 means 4 × 7, and then 3 more is added after that, so the expression is (4 × 7) + 3. Its value is 28 + 3 = 31. The parentheses show that the multiplication happens before the addition.
A composite number has a factor other than 1 and itself. Since 51 = 3 × 17, it has factors 3 and 17, so it is composite. Being odd does not make a number prime; only having exactly two factors does.
The factors of 18 are 1, 2, 3, 6, 9, and 18; the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The largest factor the two lists share is 6. So the greatest common factor is 6.
Each number is 3 times the number before it. Continuing: 54, 162, 486, 1,458, 4,374, 13,122, 39,366, so the tenth term is 39,366. Counting carefully shows 54 is the fourth term, and six more multiplications by 3 are needed.
Both points have x-coordinate 2, so they lie on the same vertical line. The distance is the difference of the y-coordinates: 7 − 3 = 4 units. Moving along a vertical line changes only the y-value.
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides, and in the exact-one-pair sense it has just one such pair. Squares, rhombuses, and rectangles all have two pairs of parallel sides. So only a trapezoid fits the description.
An obtuse angle measures more than 90 degrees and less than 180 degrees, and 125 falls in that range. A right angle is exactly 90 degrees, an acute angle is less than 90 degrees, and a straight angle is 180 degrees.
A square has four lines of symmetry: one horizontal, one vertical, and two diagonals. Folding along any of these lines makes the halves match exactly. A non-square rectangle has only two, which helps show why the square is different.
The perimeter of a rectangle is 2 × (length + width). Half of 30 is 15, so length + width = 15. Subtracting the length gives width = 15 − 9 = 6 centimeters. Checking: 2 × (9 + 6) = 30.
The first rectangle has area 8 × 5 = 40 square inches. The second rectangle must also have area 40, so its width is 40 ÷ 10 = 4 inches. Equal areas do not require equal side lengths.
The area of the first rectangle is 6 × 4 = 24 square units, and the area of the second is 3 × 4 = 12 square units. Adding them gives 24 + 12 = 36 square units, since the joined edges are not part of the outside area.
A pencil is a small object, so centimeters give a number that is easy to work with. Meters would give a fraction much less than 1, and kilometers are far too large for a classroom object. Kilograms measure mass, not length.
Since 1 liter equals 1,000 milliliters, 2 liters equals 2,000 milliliters. Subtracting gives 2,000 − 750 = 1,250 milliliters. Converting to a single unit first keeps the subtraction straightforward.
Ben read 9 books and Cara read 4 books. The difference is 9 − 4 = 5 books. Comparing two bars means subtracting the smaller value from the larger one.
Because the sections are equal in size, the chance of each color depends on how many sections it covers. Blue covers 5 of 8 sections and red covers 3 of 8, so blue is more likely. Since red covers 3 sections, it is possible, not impossible.
Numbers that round to 700 to the nearest ten are from 695 through 704. The only choice inside that range is 694? No: 694 rounds to 690, so the correct choice is 706? Check: 706 rounds to 710. The value in range is 695 to 704, and among the choices only 694 is closest to 690, so rechecking shows 706 rounds to 710 and 714 rounds to 710, leaving no listed value except one that must be 694, which rounds to 690.
Rewrite 1/2 as 4/8 so both fractions have the same denominator. Then 3/8 + 4/8 = 7/8. Denominators are not added; only the numerators are added once the denominators match.
The notebooks cost 4 × $2 = $8 and the pens cost 2 × $3 = $6, for a total of $14. Subtracting from $20 gives $20 − $14 = $6 in change. Finding the total cost first keeps the two steps separate.
Apply the rule in order: 7 × 6 = 42, then 42 − 9 = 33. Order matters because the subtraction happens after the multiplication, not before it.