5A Cumulative Semester Review

A city's population is 608,040,207. Write it in words, identify the value of the 8, and compare it with 608,400,207. Show a mathematical method and explain or check your result. Include any appropriate units.

A museum sold 3,407 tickets each day for 100 days. How many tickets is that? Explain the place-value shift. Show a mathematical method and explain or check your result. Include any appropriate units.

84,500 stickers are boxed equally into 100 cartons. How many per carton? Explain whether there is a remainder. Show a mathematical method and explain or check your result. Include any appropriate units.

Calculate 430 × 60 by splitting the tens and hundreds. Explain each factor. Show a mathematical method and explain or check your result. Include any appropriate units.

The warehouse ships 78,000 pencils in cartons of 300. How many cartons? Check by multiplication. Show a mathematical method and explain or check your result. Include any appropriate units.

A food bank receives 640 cartons of 250 packages and ships the packages evenly to 100 centers. Find the packages per center. Explain both operations. Show a mathematical method and explain or check your result. Include any appropriate units.

Evaluate 8×6 + 14÷2 and (8×6 + 14)÷2. Draw or describe an operation tree for each expression and explain which quantities are divided by two. Show a mathematical method and explain or check your result. Include any appropriate units.

Evaluate 74 − 6 × (3 + 5), and explain which operation comes first. Show a mathematical method and explain or check your result. Include any appropriate units.

Evaluate 96 ÷ (4 × 2) + 35 ÷ 7 − 3 and write the sequence of operations. Show a mathematical method and explain or check your result. Include any appropriate units.

Write two different but equivalent expressions for five groups of (12 + 3) counters and evaluate both. Show a mathematical method and explain or check your result. Include any appropriate units.

Three buses carry 28 pupils each, and 17 pupils travel by car. Write one expression and find the total. Show a mathematical method and explain or check your result. Include any appropriate units.

A class orders 5 packs with 16 markers each, gives away 22 markers, then divides the rest equally among 2 rooms. Write one expression and find the markers per room. Show a mathematical method and explain or check your result. Include any appropriate units.

A coach buys 4 bags of (12 balls + 3 cones). An assistant incorrectly writes 4×12+3=51. Explain the missing grouping, write the correct expression, and evaluate. Show a mathematical method and explain or check your result. Include any appropriate units.

Find 34×26 by showing all four place-value partial products. Show a mathematical method and explain or check your result. Include any appropriate units.

Calculate 68×45 with an efficient vertical or partial-products method and estimate to check. Show a mathematical method and explain or check your result. Include any appropriate units.

Calculate 5,760 ÷ 80 using an equivalent smaller division. Verify. Show a mathematical method and explain or check your result. Include any appropriate units.

A 2-digit number is divided by 14 and gives 6 remainder 3. Find the dividend and explain why the remainder is valid. Show a mathematical method and explain or check your result. Include any appropriate units.

Divide 936 by 24. Show a quotient check with multiplication. Show a mathematical method and explain or check your result. Include any appropriate units.

Find 745÷28 as quotient and remainder; use multiplication to confirm. Show a mathematical method and explain or check your result. Include any appropriate units.

Calculate 3,864÷42. Explain the tens and ones of the quotient. Show a mathematical method and explain or check your result. Include any appropriate units.

A club orders 38 packs of 24 beads. Divide the total beads evenly among 12 groups. How many beads per group? Show the multiplication and division. Show a mathematical method and explain or check your result. Include any appropriate units.

A printer makes 2,548 labels. Each sheet holds 36 labels. How many complete sheets can be filled, and how many labels remain? Verify. Show a mathematical method and explain or check your result. Include any appropriate units.

Seven identical flatbreads are shared equally among 12 campers. How much flatbread does each get? Write a division sentence and simplified fraction. Show a mathematical method and explain or check your result. Include any appropriate units.

Calculate 2/3 + 3/8 using common-sized parts; simplify. Show a mathematical method and explain or check your result. Include any appropriate units.

Compute 7/10 − 1/4 and explain the common denominator. Show a mathematical method and explain or check your result. Include any appropriate units.

Add 2 1/5 + 3 3/10 and explain the fractional renaming. Show a mathematical method and explain or check your result. Include any appropriate units.

Calculate 4 5/6 + 1 3/4. Show the fraction regrouping as a whole. Show a mathematical method and explain or check your result. Include any appropriate units.

Subtract 6 7/9 − 2 1/3. Explain whether a whole must be exchanged. Show a mathematical method and explain or check your result. Include any appropriate units.

Find 5 1/4 − 2 5/8, demonstrating the one-whole exchange. Show a mathematical method and explain or check your result. Include any appropriate units.

A liter jug has 7/12 L of orange juice. Add 5/18 L of apple juice, then pour out 1/6 L. How much is left? Show common denominators. Show a mathematical method and explain or check your result. Include any appropriate units.

A baker has 6 1/6 kg of dough and uses 2 5/12 kg for rolls plus 1 3/4 kg for loaves. How much remains? Show a common denominator and one exchange. Show a mathematical method and explain or check your result. Include any appropriate units.

A ribbon segment is 3/5 m. Five segments are placed end to end. How long? Explain repeated groups. Show a mathematical method and explain or check your result. Include any appropriate units.

Find 3/8 of 56 pencils by identifying eight equal groups. Show a mathematical method and explain or check your result. Include any appropriate units.

There are 48 garden stakes. Two-thirds are wooden. How many wooden stakes, and what is the original whole? Show a mathematical method and explain or check your result. Include any appropriate units.

Shade 1/3 of 3/4 of a rectangle using a 3-by-4 partition; what part of the whole is covered? Show a mathematical method and explain or check your result. Include any appropriate units.

An artist colors 3/7 of the rows and 2/5 of the columns in a 7×5 grid. What fraction lies in both colored groups? Show a mathematical method and explain or check your result. Include any appropriate units.

Calculate 7/12 × 8/21. Use cross-cancellation and show the remaining factors. Show a mathematical method and explain or check your result. Include any appropriate units.

Compute 1 2/3 × 2 1/4. Estimate first, then multiply improper fractions. Show a mathematical method and explain or check your result. Include any appropriate units.

A jar holds 90 beads. You use 2/5 of them, then 1/3 of the beads remaining. How many remain? Show a mathematical method and explain or check your result. Include any appropriate units.

Write the reciprocal of 5/12 and verify their product is one. Explain why zero has no reciprocal. Show a mathematical method and explain or check your result. Include any appropriate units.

In a garden, 3/8 of 64 plants are flowers. Of those flowers, 1/3 are yellow. How many yellow flowers are there? Identify each whole. Show a mathematical method and explain or check your result. Include any appropriate units.

A chef needs 2 1/4 cups of flour per loaf. What amount is needed for 1 2/3 loaves? Express an exact mixed number and a reasonable estimate. Show a mathematical method and explain or check your result. Include any appropriate units.

Three-quarters of a cup is split into 6 equal servings. How much is each serving? Show a mathematical method and explain or check your result. Include any appropriate units.

A 5/6 L juice portion is shared equally into 5 glasses. Find liters per glass and check. Show a mathematical method and explain or check your result. Include any appropriate units.

How many 1/6-meter pieces fit into a 4-meter cord? Explain using equal groups. Show a mathematical method and explain or check your result. Include any appropriate units.

How many 3/4-L portions fit into 6 L? Explain what the quotient counts. Show a mathematical method and explain or check your result. Include any appropriate units.

Compare these situations: (A) share 3/5 L equally among three cups; (B) count 1/5-L cups in 3 L. Give both answers with units and explain why they differ. Show a mathematical method and explain or check your result. Include any appropriate units.

Two-fifths of a kilogram of berries are shared equally among 8 bowls. How many grams of berries are in each bowl? Show a mathematical method and explain or check your result. Include any appropriate units.

A restaurant owns 5 L of sauce. It pours 3/4 L into each serving container. How many full containers and how much sauce is left? Show a mathematical method and explain or check your result. Include any appropriate units.

Convert 2 3/4 meters to centimeters, then explain why the conversion is exact. Show a mathematical method and explain or check your result. Include any appropriate units.

A rectangle measures 2 1/4 m by 1 1/3 m. Find its exact area, with square units. Show a mathematical method and explain or check your result. Include any appropriate units.

A triangular sign has base 18 cm and perpendicular height 7 cm. Find its area. Explain the factor 1/2. Show a mathematical method and explain or check your result. Include any appropriate units.

An obtuse triangle has a horizontal 12-cm base; its perpendicular altitude to the extended base is 5 cm. Calculate its area and explain why the altitude may fall outside. Show a mathematical method and explain or check your result. Include any appropriate units.

A 14 m × 9 m rectangle has a 4 m × 3 m rectangular corner removed. Find the remaining area without counting any region twice. Show a mathematical method and explain or check your result. Include any appropriate units.

A floor tile measures 3/4 m by 2/5 m. Find its exact area in cm². Show the m²-to-cm² conversion. Show a mathematical method and explain or check your result. Include any appropriate units.

A rectangular park section measures 20 m by 12 m. A triangle with base 8 m and perpendicular height 12 m is removed. Find the remaining area. Show a mathematical method and explain or check your result. Include any appropriate units.

A crate is filled with 4 layers of unit cubes. Each layer has 3 rows of 5 cubes. How many unit cubes in all? State the cubic-unit measurement. Show a mathematical method and explain or check your result. Include any appropriate units.

A cuboid is 12 cm long, 5 cm wide, and 3 cm high. Calculate volume and explain the layer count. Show a mathematical method and explain or check your result. Include any appropriate units.

A cuboid has volume 420 cm³, length 10 cm, and height 7 cm. Find its missing width. Show a mathematical method and explain or check your result. Include any appropriate units.

Two nonoverlapping cuboids have dimensions 6×4×3 cm and 5×2×4 cm. Find their combined volume, identifying both parts. Show a mathematical method and explain or check your result. Include any appropriate units.

A container holds 2,750 cm³ of water. Convert this capacity to mL and to liters. State the equivalence used. Show a mathematical method and explain or check your result. Include any appropriate units.

A rectangular aquarium measures internally 25 cm by 16 cm by 20 cm. How many liters are needed to fill it completely? Show a mathematical method and explain or check your result. Include any appropriate units.

A cuboid has volume 1,200 cm³, width 10 cm, and height 8 cm. A second cuboid has dimensions 5×4×3 cm. Find the missing length and their combined volume. Show a mathematical method and explain or check your result. Include any appropriate units.

A tank measures internally 50×20×16 cm. It is three-quarters full. How many liters must be added to fill it? Show a mathematical method and explain or check your result. Include any appropriate units.