Unit 3
Pecahan Setara
Kai Xin dan Ravi ada wafer yang sama panjang.
Wafer Kai Xin dipotong 4 bahagian sama besar. Dia makan 1 bahagian.
Wafer Ravi dipotong 8 bahagian sama besar. Dia makan 2 bahagian.
Siapa makan lebih banyak?
等值分数 = pecahan setara
两块一样长的威化饼，一块切 4 等份吃 1 份，另一块切 8 等份吃 2 份。切得越细，每份越小，所以 2 小份可能和 1 大份一样多。这一单元学怎么判断两个分数是不是一样大。
例子：一张饼分 2 份吃 1 份，和分 6 份吃 3 份，吃得一样多。
注意：比较时两个整体要一样大。
equivalent fractions = pecahan setara
Two wafers of the same length: one is cut into 4 equal pieces with 1 eaten, the other into 8 with 2 eaten. Smaller pieces mean 2 small pieces may equal 1 big piece. This unit shows how to tell if two fractions are the same amount.
Example: 1 of 2 pieces of a flatbread and 3 of 6 pieces are the same amount.
Watch out: the two wholes must be the same size when you compare.
Pecahan setara
Berbeza tetapi sama nilai
Bahagian berwarna sama panjang
PECAHAN SETARA
Pecahan yang ditulis berbeza tetapi nilainya sama.
14 setara dengan 28.
Pecahan yang ditulis berbeza tetapi nilainya sama.
14 setara dengan 28.
看长条比较 = banding dengan jalur
两条一样长的长条：上面 4 等份涂 1 份，下面 8 等份涂 2 份。涂色部分的末端对齐，长度一样，所以 1/4 和 2/8 一样大。写法不同但数值相同的分数，叫做等值分数。
例子：3 等份涂 1 份和 9 等份涂 3 份对齐 → 1/3 与 3/9 等值。
注意：两条长条一定要一样长，比较才公平。
comparing with strips = banding dengan jalur
The top strip has 4 equal parts with 1 shaded; the bottom one has 8 with 2 shaded. The shading ends at the same place, so 1/4 and 2/8 are the same size. Fractions written differently with the same value are equivalent.
Example: 1 of 3 parts lines up with 3 of 9 parts → 1/3 and 3/9 are equivalent.
Watch out: both strips must be the same length for a fair comparison.
Cari pecahan setara
Darab dengan nombor yang sama
Pengangka dan penyebut
1 × 24 × 2 = 28
Setiap bahagian dipotong dua.
Bilangan bahagian berwarna dan jumlah bahagian kedua-duanya × 2.
同乘一个数 = darab dengan nombor yang sama
把分子和分母乘同一个数，得到的分数和原来的一样大。1/4 的分子分母都乘 2，得到 2/8。想象把每一份再切成 2 小份：总份数变成 2 倍，涂色的份数也变成 2 倍。
例子：2/5 → 分子分母都乘 2 → 4/10。
注意：只乘分子或只乘分母，大小就改变了。
multiply by the same number = darab dengan nombor yang sama
Multiply the numerator and the denominator by the same number and the new fraction has the same value. For 1/4, multiply both by 2 to get 2/8. Picture cutting every part into 2 smaller pieces: the total parts double and the shaded parts double too.
Example: 2/5 → multiply both by 2 → 4/10.
Watch out: multiplying only the top or only the bottom changes the size.
Bandingkan jalur pecahan
Pilih pecahan pada jalur bawah. Perhatikan sama ada bahagian berlorek sama panjang.
分数条 = jalur pecahan；等值 = setara；涂色部分 = bahagian berlorek
上面的分数条固定显示二分之一，下面可以切成 4、6 或 8 等份。选择不同分数后，比较两条涂色部分的长度；虽然格数和每格大小不同，只要覆盖长度相同，两个分数就是等值分数。
例子：把每一个二分之一再切成两小份，就会看到二分之一与四分之二同样长。
注意：只数涂色格不够，还要同时看整条被分成多少份。
fraction strip = jalur pecahan; equivalent = setara; shaded part = bahagian berlorek
The upper strip always shows one half. The lower strip can be divided into 4, 6 or 8 equal parts. Choose a fraction and compare the shaded lengths. The number and size of the boxes may differ, but equal covered lengths mean the fractions are equivalent.
Example: split each half into two smaller parts and one half becomes two quarters with exactly the same length.
Watch out: counting shaded boxes alone is not enough; also check how many equal parts make the whole strip.
Semak makmal
Bagaimanakah dua jalur menunjukkan pecahan setara?
怎样判断 = bagaimana menentukan；同样长 = sama panjang
题目请你说明怎样从两条分数条判断它们等值。回想实验台：格数会改变，颜色只是为了看得清楚，真正要比较的是从同一个起点开始，涂色覆盖到哪里。请选择符合这个观察的说法。
例子：可以把两条纸带左端对齐，再比较涂色终点是否对齐。
注意：格数相同并不是等值的必要条件，颜色也不会改变分数大小。
how to determine = bagaimana menentukan; same length = sama panjang
The question asks how the strips demonstrate equivalent fractions. Recall that the number of boxes changed in the lab and colour only helped visibility. What mattered was where the shaded part ended when both strips began at the same point. Choose the statement that matches that observation.
Example: align the left ends of two paper strips and compare whether the shaded endpoints line up.
Watch out: the strips do not need the same number of boxes, and colour does not change a fraction's value.
Cuba
Pecahan manakah setara dengan 35?
用乘法找等值分数 = cari pecahan setara dengan darab
要找和 3/5 一样大的分数，就把分子和分母乘同一个数。分母不能超过 10，所以想一想：5 乘几还不超过 10？用同一个数也乘上面的分子。
例子：1/5 × 2/2 → 2/10。
注意：分子和分母一定要乘同一个数，只乘其中一个，大小就改变了。
finding an equivalent by multiplying = cari pecahan setara dengan darab
To find a fraction equal to 3/5, multiply the numerator and the denominator by the same number. The denominator stays at 10 or less, so ask what 5 can be multiplied by, and use the same number on the top.
Example: 1/5, both times 2 → 2/10.
Watch out: the top and bottom must be multiplied by the same number; changing only one of them changes the size.
Adakah 39 setara dengan 13?
Cara 1: Lukis jalur
Bandingkan panjang bahagian berwarna
Bahagian berwarna sama panjang.
3 bahagian 19 = 1 bahagian 13
方法一：画长条 = Cara 1: lukis jalur
画两条一样长的长条，一条分 9 等份涂 3 份，另一条分 3 等份涂 1 份。如果两条涂色的部分一样长，两个分数就等值。这里 3 小格刚好等于 1 大格。
例子：10 等份涂 6 份与 5 等份涂 3 份对齐 → 6/10 与 3/5 等值。
注意：格子要画得平均，不然看不准。
method 1: draw strips = Cara 1: lukis jalur
Draw two strips of the same length, one cut into 9 equal parts with 3 shaded and one cut into 3 with 1 shaded. If the shaded lengths match, the fractions are equivalent. Here 3 small boxes cover exactly 1 big box.
Example: 6 of 10 parts lines up with 3 of 5 parts → 6/10 and 3/5 are equivalent.
Watch out: draw the parts evenly, or the comparison will not be accurate.
Cara 2
Bahagi dengan nombor yang sama
39 → ?
3 ÷ 39 ÷ 3 = 13
39 setara dengan 13
方法二：同除一个数 = Cara 2: bahagi dengan nombor yang sama
分子分母能被同一个数整除时，可以一起除。3 和 9 都能被 3 整除：3 ÷ 3 = 1，9 ÷ 3 = 3，所以 3/9 = 1/3，就是把 3 小份合成 1 大份。
例子：4/8 → 上下都除以 4 → 1/2。
注意：选的数要能同时整除分子和分母。
method 2: divide by the same number = Cara 2: bahagi dengan nombor yang sama
When the top and bottom both divide exactly by the same number, divide both. 3 and 9 both divide by 3: 3 ÷ 3 = 1 and 9 ÷ 3 = 3, so 3/9 = 1/3. It joins 3 small parts into 1 big part.
Example: 4/8 → divide both by 4 → 1/2.
Watch out: choose a number that divides both the top and the bottom exactly.
Cuba
Adakah 26 setara dengan 12?
检查是否等值 = semak sama ada setara
可以用两种方法检查。用长条：看两条涂色部分的末端是否对齐。用除法：分子分母除以同一个数，看化出来的分数和另一个分数是否相同。
例子：6/9 和 2/3 → 6/9 上下都除以 3 → 2/3，所以等值。
注意：只除分子、不除分母，就会以为 2/6 等于 1/2。
checking equivalence = semak sama ada setara
There are two ways to check. With strips: see whether the shaded parts end at the same place. With division: divide the top and bottom by one number and see whether the result matches the other fraction.
Example: 6/9 and 2/3 → divide 6/9 by 3 on top and bottom → 2/3, so they are equivalent.
Watch out: dividing only the numerator makes 2/6 look like 1/2.
Carta pecahan
Pecahan setara bagi 23
Ikut garis merah ke bawah
23 = 46 = 69
分数墙 = carta pecahan
分数墙每一行都和整体 1 一样长，分别分成 3、6、9 等份。从 2/3 的末端往下画一条直线，看看哪一行的格子也刚好停在这条线上：6 份那一行停在第 4 格，9 份那一行停在第 6 格。所以 2/3 = 4/6 = 6/9。
例子：3/3 往下看 → 6/6、9/9，都等于 1。
注意：线必须刚好落在格子的边上才算。
fraction wall = carta pecahan
Every row of the wall is as long as 1 whole, cut into 3, 6 and 9 equal parts. Draw a line down from the end of 2/3 and see which rows also stop exactly on that line: sixths stop after 4 parts and ninths after 6. So 2/3 = 4/6 = 6/9.
Example: follow 3/3 down → 6/6 and 9/9, which all equal 1.
Watch out: the line must land exactly on the edge of a box to count.
Guna carta
Ikut garis merah. Pecahan manakah setara dengan 25?
看分数墙找等值 = cari pecahan setara dengan carta
分数墙的每一行都和整体 1 一样长。沿着红色虚线往下看到十分之几那一行，数一数虚线左边有几格，这就是新的分子；那一行一共分几格，就是新的分母。
例子：2/4 往下对齐八分之几那一行，左边有 4 格 → 4/8。
注意：不要直接抄原来的分子，要真的数格子。
using the wall to find an equivalent = cari pecahan setara dengan carta
Every row of the wall is as long as 1 whole. Follow the red dashed line down to the tenths row and count the boxes to the left of the line; that count is the new numerator, and the number of boxes in the row is the new denominator.
Example: 2/4 followed down to the eighths row has 4 boxes to the left → 4/8.
Watch out: do not just copy the old numerator; really count the boxes.
Pola nombor
Lihat pengangka dan penyebut
23 = 46 = 69
| × 1 | × 2 | × 3 | |
|---|---|---|---|
| pengangka | 2 | 4 | 6 |
| penyebut | 3 | 6 | 9 |
2 × 33 × 3 = 69
等值分数的规律 = pola pecahan setara
把 2/3、4/6、6/9 排在一起：分子每次加 2，分母每次加 3，其实就是把 2/3 的上下同乘 2、同乘 3。上下乘同一个数，就能写出新的等值分数。
例子：1/4 → 2/8（上下都乘 2）。
注意：分子每次加的是原来的分子，分母每次加的是原来的分母。
pattern in equivalent fractions = pola pecahan setara
Line up 2/3, 4/6 and 6/9: the numerators 2, 4, 6 go up by 2 each time and the denominators 3, 6, 9 go up by 3. That is 2/3 with both numbers times 2 and times 3. Multiplying top and bottom by the same number keeps giving new equivalent fractions.
Example: 1/4 → 2/8 (both times 2).
Watch out: the top grows by the first numerator each step, and the bottom by the first denominator.
Pola
Lengkapkan pola: 13, 26, 3?
找分子分母的规律 = cari pola pengangka dan penyebut
把分子和分母分开看：分子每一步加多少？分母每一步又加多少？分母每次加的数，等于第一个分数的分母。也可以想成第一个分数的上下同乘 1、2、3。
例子：1/5、2/10 → 分子加 1，分母加 5。
注意：分子每次加 1，不代表分母也只加 1。
finding the number pattern = cari pola pengangka dan penyebut
Look at the numerators and the denominators separately: how much does the top grow each step, and how much does the bottom grow? The bottom grows by the first denominator each time. You can also think of it as the first fraction times 1, 2 and 3 on top and bottom.
Example: 1/5, 2/10 → the top grows by 1 and the bottom by 5.
Watch out: the top growing by 1 does not mean the bottom grows by 1.
Padankan
Pasangan setara
配对等值分数 = padankan pecahan setara
看左边每个分数：分子分母能不能同乘或同除一个数，变成右边的分数？先看分子分母是不是都能被 2 或 3 整除。
例子：1/2 → 上下都乘 3 → 3/6。
注意：上下要用同一个数，不可以一个乘 2、一个乘 3。
matching equivalent pairs = padankan pecahan setara
For each fraction on the left, ask whether multiplying or dividing its top and bottom by the same number gives a fraction on the right. Try 2 or 3 first and see whether it divides both numbers exactly. The number that works on top and bottom shows the match.
Example: 1/2 → both times 3 → 3/6.
Watch out: use one number for both; never times 2 on top and times 3 below.
Pilih dan sebut
Pilih pecahan setara bagi 46.
选出等值分数 = pilih pecahan setara
找一个能同时整除分子和分母的数，上下一起除，就得到一个分母比较小的等值分数。也可以反过来检查：把选项的上下乘同一个数，看能不能回到 4/6。
例子：6/8 → 上下都除以 2 → 3/4。
注意：分子分母各加上同一个数，并不会得到等值分数。
choosing an equivalent = pilih pecahan setara
Find a number that divides both the top and the bottom exactly and divide both by it to get an equivalent with a smaller denominator. Check it the other way too: multiply a choice's top and bottom by one number and see if you get back to 4/6.
Example: 6/8 → both divided by 2 → 3/4.
Watch out: adding the same number to the top and bottom does not give an equivalent fraction.
Ringkasan
Syabas!
23 = 46 = 69
Pecahan setara ialah pecahan berbeza yang sama nilai. Darab atau bahagi pengangka dan penyebut dengan nombor yang sama.
Latihan tambahan →