All the solutions provided in McGraw Hill My Math Grade 4 Answer Key PDF Chapter 2 Add and Subtract Whole Numbers will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 2 Add and Subtract Whole Numbers
What strategies can I use to add or subtract?
Answer: We can use split strategy , jump strategy , make to the next ten strategy
1. Split strategy : This is sometimes called the decomposition, partitioning or partial-sums strategy.
You can add or subtract the tens separately to the ones (or units).
For example, using the split strategy to add 46 + 23, you would,
split each number (decompose) into tens and ones: 46 + 23 = 40 + 6 + 20 + 3,
rearrange the tens and ones: 40 + 20 + 6 + 3,
add the tens and then the ones 60 + 9 = 69.
For subtraction : such as 69 – 46, you would,
split or decompose each number into tens and ones: 60 + 9 – (40 + 6)
remove bracket: 60 + 9 – 40 – 6,
rearrange tens and ones: (60 – 40) + (9 – 6),
subtract the tens, then the ones: 20 + 3 = 23.
2. Jump strategy : This is sometimes called the sequencing or cumulative sums strategy.
For example, adding 46 + 23 using the jump strategy might look like this,
add two lots of ten to 46: 46 + 10 = 56, then 56 + 10 = 66
add the remaining 3: 66 + 3 = 69
add 20 to 46 which becomes 66
add the remaining 3: 66 + 3 = 69
For subtraction :
Subtracting 69 – 46 with the jump strategy could be done by,
subtracting four lots of ten (40) from 69: 69 – 10 = 59; 59 – 10 = 49; 49 – 10 = 39; 39 – 10 = 29
then finally subtracting the remaining 6: 29 – 6 = 23
subtract 40: 69 – 40 = 29
then subtract 6: 29 – 6 = 23
3. ‘Make to the next ten’ strategy: This is sometimes called the compensation or shortcut strategy. It involves adjusting one number to make the task easier to solve.
create all the combinations of two single digit numbers that give a total of ten.
9 + 1, 8 + 2, 7 + 3, 6 + 4, 5 + 5 …
So, to add 37 + 65, you would,
add 3 to 37 to give 40.
subtract 3 from 65 to get 6,
this becomes: 40 + 62 = 102.
If subtracting 102 – 65, you would,
subtract 2 from 102 to make 100
subtract 2 from 65 to maintain the balance
this becomes 100 – 63 = 37.
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The property which states that the order in which two numbers are added does not change the sum.
Imagine you need to shop for many items. Describe how this property could be used when estimating the sum.
Answer: Commutativity of addition.
The order of the two numbers does not affect their sum: 3+5=8=5+3.
For example, If we have to buy a pen, pencil, book which costs 10, 5, 20 /- respectively
Then the order of adding them can be anything like 10 + 5 + 20 or 5 + 10 + 20 or 20 + 5 + 10 or 10 + 20 +5
no matter the order the answer will be same that is 10 + 5 + 20 = 35
So, The property which states that the order in which two numbers are added does not change the sum is Commutative property
For any number, zero plus that number is the number.
Look in the dictionary for a meaning of identity. Write a sentence using that meaning.
Answer: Identity property of addition
The additive identity property is also known as the identity property of addition, which states that adding 0 to any number, results in the number itself.
Simply, For any number, zero plus that number is the number is called Identity property of addition
A number subtracted from another number.
Write a tip to help you remember which number is the minuend and which is the subtrahend.
Answer: The number which is larger or greater is the number from which another number is going to be substracted is called minuend
The number which is smaller than the number from which it is substracted is called subtrahend.
For Example, 53 – 13, where 53 is the minuend and 13 is the subtrahend
74 – 22, in this case, 34 is the minuend 22 is the subtrahend
So, Subtrahend is defined as the number being subtracted from another and the number from which another number is being subtracted is known as the minuend.
A letter or symbol used to represent an unknown quantity.
Variable can mean changeable. Explain how this relates to the math meaning of variable.
Answer: In math , a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity.
The variables are specially used in the case of algebraic expression or algebra.
For example, x+9=4 is a linear equation
where x is a variable, where 9 and 4 are constants.
Here, A letter or symbol used to represent an unknown quantity is called Variable
The property which states that the grouping of the addends does not change the sum.
Associate can mean “to combine or come together.” Explain how this helps you understand this property.
Answer: Associative property
The associative property states that the sum of three or more numbers does not change, if they are grouped in a different way.
This associative property is applicable to addition , It is expressed as, (A + B) + C = A + (B + C)
Thus, The property which states that the grouping of the addends does not change the sum is called Associative property.
A sentence that contains an equals sign (=), showing that two expressions are equal.
Explain how an equation is different than an expression
Answer: An expression is a mathematical phrase that contains numbers, variables, or both. An equation is made up of two expressions connected by an equal sign.
Expressions never have an equal sign. Here are some examples of expressions.
An equation is a mathematical sentence that says two expressions are equal.
Word example: The sum of 8 and 3 is equal to 11.
The order of the two numbers does not affect their sum: 5 + 5 = 10 = 6 + 4.
So, A sentence that contains an equals sign (=), showing that two expressions are equal , whether meaningfully or numerically.
The number from which another number is subtracted.
What word from this chapter is also a part of a subtraction equation, other than minuend?
Answer: subtrahend, The number which is smaller than the number from which it is substracted is called subtrahend.
For example, 748 – 100 , Here 100 is the subtrahend.
So, The number from which another number is subtracted, or the number which is smaller than the other number being subtracted is called subtrahend.
An amount that has not been identified.
The prefix un- means “not”. Name two other words with this prefix.
Answer: uncommon and unidentified .
The term or the missing information which has to be found out after calculating the problem is called as unknown quantity
For example , 10 – 5 + ? = 10, ? = 5
Then the equation will be balanced
What number here given, will replace the question mark is the amount that has not been identified.
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