## COMMON WHOLE NUMBER PROBLEM SUMS

###### DIFFERENCE CONCEPT

John can bake 3 cupcakes in an hour. Peter can bake 5 cupcakes in an hour. John has 8 more cupcakes than Peter. If they start baking at the same time, how many hours later will Peter have 8 more cupcakes than John?###### SHORTAGE AND SURPLUS

John wanted to pack an equal number of stamps in 32 packets but was short of 157 stamps. He packs the same number of stamps into 24 packets and has 11 stamps left. How many stamps did John have at first?###### QUANTITY INTERNAL TRANSFER

John has $64 more than Yenni. After John gives Yenni $9, John has thrice as much money as Yenni. How much does John have at first?###### QUANTITY VALUE WITH EXTRA QUANTITY REVISION

101 cards were shared with some boys and girls. There were 4 more boys than girls. Each boy received 5 cards and each girl received 4 cards. How many boys are there?###### DISTRIBUTION OF DIFFERENCE

Ten boys were tasked to paint the chairs in an auditorium. One of them fell sick and the rest had to paint 6 more chairs each. How many chairs did they have to paint altogether?###### UNCHANGED DIFFERENCE

At first, there were 410 more men than women at an exhibition. At lunch time, a total of 250 men and women left the exhibition. There were as many men as women who left the exhibition. In the end, there were 3 times as many men as women who remained behind. How many men were at the exhibition at first?## PROBLEM SUMS THAT INVOLVE QUANTITY AND VALUE

###### QUANTITY AND VALUE INVOLVING TOTAL DIFFERENCE

There are 3/5 as many boys as girls at a party. Each boy is given 4 balloons and each girl is given 2 balloons. The total number of balloons received by the boys is 200 more than the girls. How many boys were at the party?###### QUANTITY AND VALUE INVOLVING EXTRA QUANTITY AND TOTAL DIFF IN VALUE (EXAMPLE 1)

John bought 4 more books than files. A book cost $13 and a file cost $5. If he paid $116 more for the books than the files, how many books did John buy?###### QUANTITY AND VALUE INVOLVING EXTRA QUANTITY AND TOTAL DIFF IN VALUE (EXAMPLE 2)

Peter bought 6 more chairs than tables. A table cost $36 and a chair cost $18. If he paid $396 more for the tables than the chairs, how many chairs are there?###### HOW TO SOLVE SIMULTANEOUS STATEMENTS?

Simultaneous statements were first introduced in Primary 4. This example is a Primary 5 simultaneous question. “Simultaneous concept” is arithmetic math. It is solving 2 unknowns with 2 number statements. This is a useful skill to acquire early in the year as it can be applied to solve subsequent problem sums.## EXTERNAL AND INTERNAL TRANSFER PROBLEM SUMS

###### QUANTITY EXTERNAL TRANSFER USING MODEL (EXAMPLE 1)

John and Peter had some stamps. Peter had 23 more stamps than John. After Peter gave away 57 stamps, John had thrice as many stamps as Peter. Find the number of stamps Peter had in the end.###### QUANTITY EXTERNAL TRANSFER USING MODEL (EXAMPLE 2)

John and Peter had an equal number of stickers at first. John gave away 28 of his stickers and Peter bought another 14 stickers. In the end, Peter had thrice as many stickers as John. How many stickers did John have at first?###### QUANTITY INTERNAL TRANSFER USING MODEL

John had 16 more beads than Peter at first. After John gave Peter 20 beads, Peter had 4 times as many beads as John. How many beads did John have at first?###### QUANTITY INTERNAL TRANSFER WITH SCENARIOS

John and Peter had some sticks. If John gave Peter 30 sticks, they would have an equal number of sticks. If Peter gave John 30 sticks, John would have 4 times as many sticks as Peter. How many sticks did John have?## CHALLENGING WHOLE NUMBER PROBLEM SUMS

###### VOLUME INVOLVE WORKING FORWARD/BACKWARDS

A rectangular tank measuring 30 cm by 12 cm by 16 cm contained some water. A cubical container with side measuring 12 cm is completely filled with water. All of the water from the cubical container is poured into the rectangular tank and as a result the rectangular tank became 2/3 full. What was the amount of water in the rectangular tank at first?###### DIFFERENCE UNCHANGED CONCEPT

John gets $8 more allowance than Yenni each week. Every week, each of them spends $36 on food and saves the rest. When John saves $108 Yenni saves $60.

a) How many weeks does John take to save $108?

b) How much allowance does John get each week?

###### EXCHANGE WITH INCREASE IN TOTAL

Peter had a total of 40 pens and highlighters at first. He then decided to exchange all his pens for highlighters. He exchanged each pen for 5 highlighters and had a total of 88 highlighters in the end. How many pens did he have at first?###### SIMULTANEOUS CONCEPT

A sum of money can be used to buy either 8 identical wallets or 20 identical key chains. Each wallet cost $14.40 more than each key chain. How much did each key chain cost?## FRACTIONS BASICS

###### MULTIPLICATION OF FRACTIONS

Multiplying fractions is a crucial skill for students in solving math problems in exams. Multiplying fractions accurately is essential for working with more complex math problems involving ratios, proportions, and fractions in their simplest form. To help students master this skill, this video will provide a simple step-by-step guide on how to multiply fractions, breaking down the process into easy-to-follow steps that students can apply to various exam questions.###### DIVISION OF FRACTIONS

Learning to divide fractions is important for P5, particularly when solving math problems in exams. Students must understand how to divide fractions into smaller parts to work with them accurately in various mathematical operations. This skill enables students to handle complex problems in exams, including ratios, proportions, and fractions in their simplest form. This video will provide students with a simple step-by-step guide to learning the mechanics of dividing fractions, breaking down the process into easy-to-understand steps.###### MULTIPLICATION OF MIXED NUMBER WITH A FRACTION

Learning the arithmetic mechanics of multiplication of mixed numbers with a fraction is crucial for students when it comes to solving math problems in exams. Being able to perform this operation accurately is essential when working with more complex math problems that involve fractions, ratios, and proportions. To help students, this video will provide a simple step-by-step guide on how to multiply mixed numbers with a fraction, breaking down the process into easy-to-follow steps.###### FRACTION AS UNITS VS AS MEASUREMENT

The difference between fractions as a unit of measure and fractions as a proportion is whether the fraction is being used to indicate a specific quantity or a proportion of a whole.###### REASONING FRACTIONS

I am thinking of a fraction. The difference between the numerator and the denominator is 23. When 5 is added to the denominator, the fraction becomes 1/5. What is the fraction?## FRACTIONS WITH REMAINDER PROBLEM SUMS

###### REMAINDER CONCEPT WITH + VALUES

Yenni ate 2/7 of her jellybeans on Monday. She ate 2 more jellybeans on Tuesday than on Monday. If she still had 25 jellybeans, how many jellybeans did she have at first?###### REMAINDER CONCEPT WITH +/– VALUES AND 2 BRANCHES

Yenni used 300 g more than 1/3 of the flour to bake a cake. She then used 50 g more than 1/4 of the remainder to bake tarts. If she has 700 g of flour left, how much flour did she have at first?###### REMAINDER CONCEPT WITH UNKNOWN REMAINDER 1

Peter has some savings at first. He spent $211 on a game console and 1/3 of the remainder on birthday gifts. If he had $28 in the end, how much savings did he have at first?###### REMAINDER CONCEPT WITH UNKNOWN REMAINDER 2

Yenni went shopping and spent $60 on a table. She used 3/4 of her remaining money to buy a chair. She was then left with 1/5 of her initial amount of money. How much money did she have at first?###### REMAINDER CONCEPT WITH UNKNOWN REMAINDER 3

Yenni spent $18 on food and 1/3 of the remainder on books. She saved the rest of her money, which was 4/9 of her money at first. How much did she have at first?###### PROPORTION EXTERNAL TRANSFER WITH REMAINDER THEORY

Peter spent 1/6 of his money on a pair of shoes and 1/2 of the remainder on a pair of headphones. After that, his mother gave him $1292. Now Peter has twice of his original amount of money. How much money did he have at first?###### REMAINDER THEORY

Peter spent 1/4 of his money to buy a bag. He spent 2/5 of the remainder on 4 shirts and saved the rest.

a) What fraction of Peter’s money did he spend on the 4 shirts?

b) The bag cost $168 more than one shirt. Given that the price of each shirt was the same, how much did Peter save?